I am trying to load the homescreen after the splashscreen

Check my answer from this previous post that I think will help you. You can show the splash screen and when the splash screen closes then you can show your main window. It's similar to the login window from this previous question

But if you want to keep implementing your code the way you have it I think I know the problem.

You call a method which creates the QMainWindow and calls the .show() for that QMainWindow. Once the method is done the variables in that method are garbage collected and so is your QMainWindow object. The way to keep the reference and prevent those variables from getting garbage collected is by making it a class variable by adding self. in front of the variable.

I would maybe restructure a bit and do something like this:

if __name__ == "__main__":
    app            = QApplication(sys.argv)
    splash         = SplashScreen()
    splash_closed  = splash.exec_()

    if splash_closed:                             
        window = WindowApp()   
        window.show()
        sys.exit(app.exec_())

Where the splashscreen is now a QDialog and when you're done loading you close the dialog with self.accept() instead of trying to show a new window:

class SplashScreen(QDialog):
    def __init__(self):
        super().__init__()
        self.setFixedSize(700, 350)
        self.setWindowFlag(Qt.FramelessWindowHint)
        self.setAttribute(Qt.WA_TranslucentBackground)
        self.counter = 0
        self.n = 100
        self.initUI()
        self.timer = QTimer()
        self.timer.timeout.connect(self.loading)
        self.timer.start(30)

    def initUI(self):
        ...

    def loading(self):
        # set progressbar value
        self.progressBar.setValue(self.counter)
        # stop progress if counter
        # is greater than n and
        # display main window app
        if self.counter >= self.n:
            self.timer.stop()
            self.accept()

        self.counter += 1

And you should also use the __init__ method on your main window and maybe move all the self.setupUI code in there, or just do something like this:

class WindowApp(QMainWindow):
    def __init__(self):
        QtWidgets.QDialog.__init__(self)                                                        
        self.setupUi(self)
    
    def setupUi(self, MainWindow):
        MainWindow.setObjectName("MainWindow")
        MainWindow.resize(1006, 654)

        self.centralwidget = QtWidgets.QWidget(MainWindow)
        self.centralwidget.setObjectName("centralwidget")

Hope this helps

import sys
from PyQt5.QtWidgets import QMainWindow, QDialog, QApplication
from PyQt5.QtWidgets import QPushButton, QVBoxLayout, QFrame, QLabel, QProgressBar
from PyQt5.QtWidgets import QWidget
from PyQt5 import QtCore, QtGui
from PyQt5 import QtWidgets
from PyQt5.QtCore import Qt, QTimer

class SplashScreen(QWidget):
    def __init__(self):
        super().__init__()
        self.setFixedSize(700, 350)
        self.setWindowFlag(Qt.FramelessWindowHint)
        self.setAttribute(Qt.WA_TranslucentBackground)
        self.counter = 0
        self.n = 100
        self.initUI()
        self.timer = QTimer()
        self.timer.timeout.connect(self.loading)
        self.timer.start(30)

    def initUI(self):
        # layout to display splash scrren frame
        layout = QVBoxLayout()
        self.setLayout(layout)
        # splash screen frame
        self.frame = QFrame()
        layout.addWidget(self.frame)
        # splash screen title
        self.title_label = QLabel(self.frame)
        self.title_label.setObjectName('title_label')
        self.title_label.resize(690, 120)
        self.title_label.move(0, 5)  # x, y
        self.title_label.setText('Splash Screen')
        self.title_label.setAlignment(Qt.AlignCenter)
        # splash screen title description
        self.description_label = QLabel(self.frame)
        self.description_label.resize(690, 40)
        self.description_label.move(0, self.title_label.height())
        self.description_label.setObjectName('desc_label')
        self.description_label.setText('<b>Splash Screen PyQt-5</b>')
        self.description_label.setAlignment(Qt.AlignCenter)
        # splash screen pogressbar
        self.progressBar = QProgressBar(self.frame)
        self.progressBar.resize(self.width() - 200 - 10, 50)
        self.progressBar.move(100, 180)  # self.description_label.y()+130
        self.progressBar.setAlignment(Qt.AlignCenter)
        self.progressBar.setFormat('%p%')
        self.progressBar.setTextVisible(True)
        self.progressBar.setRange(0, self.n)
        self.progressBar.setValue(20)
        # spash screen loading label
        self.loading_label = QLabel(self.frame)
        self.loading_label.resize(self.width() - 10, 50)
        self.loading_label.move(0, self.progressBar.y() + 70)
        self.loading_label.setObjectName('loading_label')
        self.loading_label.setAlignment(Qt.AlignCenter)
        self.loading_label.setText('Loading...')
        self.show()


    def loading(self):
        # set progressbar value
        self.progressBar.setValue(self.counter)
        # stop progress if counter
        # is greater than n and
        # display main window app
        if self.counter >= self.n:
            self.timer.stop()
            '''
            self.close()
            MainWindow = QtWidgets.QMainWindow()
            ui = WindowApp()
            ui.setupUi(MainWindow)
            MainWindow.show()
            '''
            self.ui = WindowApp()
            self.ui.show()
            self.close()

        self.counter += 1

class WindowApp(QMainWindow):
    def setupUi(self, MainWindow):
        MainWindow.setObjectName("MainWindow")
        MainWindow.resize(1006, 654)

        self.centralwidget = QtWidgets.QWidget(MainWindow)
        self.centralwidget.setObjectName("centralwidget")

        self.label = QtWidgets.QLabel(self.centralwidget)
        self.label.setGeometry(QtCore.QRect(10, 10, 981, 641))
        font = QtGui.QFont()
        font.setFamily("Arial")
        font.setPointSize(10)
        self.label.setFont(font)
        self.label.setText("")
        self.label.setPixmap(QtGui.QPixmap("../pygui/Homescreen.png"))
        self.label.setScaledContents(True)
        self.label.setWordWrap(False)
        self.label.setObjectName("label")

        self.infoBtn = QtWidgets.QPushButton(self.centralwidget)
        self.infoBtn.setGeometry(QtCore.QRect(120, 550, 181, 41))
        font = QtGui.QFont()
        font.setFamily("Arial")
        font.setPointSize(15)
        self.infoBtn.setFont(font)
        self.infoBtn.setStyleSheet("border-radius: 10px;\n"
                                   "border-color: 2px solid gray;\n"
                                   "background-color: rgb(255, 255, 255);")
        icon = QtGui.QIcon()
        icon.addPixmap(QtGui.QPixmap("icons/info_icon.png"),
                       QtGui.QIcon.Normal, QtGui.QIcon.Off)
        self.infoBtn.setIcon(icon)
        self.infoBtn.setObjectName("infoBtn")

        self.startBtn = QtWidgets.QPushButton(self.centralwidget)
        self.startBtn.setGeometry(QtCore.QRect(310, 270, 431, 111))
        font = QtGui.QFont()
        font.setFamily("Arial")
        font.setPointSize(28)
        self.startBtn.setFont(font)
        self.startBtn.setStyleSheet("background-color: #305E6C;\n"
                                    "color: white;\n"
                                    "border-radius: 10px;\n"
                                    "border: 2px solid white")
        self.startBtn.setObjectName("startBtn")

        self.contactsBtn = QtWidgets.QPushButton(self.centralwidget)
        self.contactsBtn.setGeometry(QtCore.QRect(720, 30, 101, 101))
        self.contactsBtn.setStyleSheet("\n"
                                       "background-color: #121212;\n"
                                       "border-radius: 50%;\n"
                                       "border: 2px solid white;")
        self.contactsBtn.setText("")
        icon1 = QtGui.QIcon()
        icon1.addPixmap(QtGui.QPixmap("icons/typcn_contacts.png"),
                        QtGui.QIcon.Normal, QtGui.QIcon.Off)
        self.contactsBtn.setIcon(icon1)
        self.contactsBtn.setIconSize(QtCore.QSize(40, 40))
        self.contactsBtn.setObjectName("contactsBtn")

        self.dateBtn = QtWidgets.QPushButton(self.centralwidget)
        self.dateBtn.setGeometry(QtCore.QRect(840, 30, 101, 101))
        self.dateBtn.setStyleSheet("\n"
                                   "background-color: #121212;\n"
                                   "border-radius: 50%;\n"
                                   "border: 2px solid white;")
        self.dateBtn.setText("")
        icon2 = QtGui.QIcon()
        icon2.addPixmap(QtGui.QPixmap("icons/Group.png"),
                        QtGui.QIcon.Normal, QtGui.QIcon.Off)
        self.dateBtn.setIcon(icon2)
        self.dateBtn.setIconSize(QtCore.QSize(40, 40))
        self.dateBtn.setObjectName("dateBtn")

        MainWindow.setCentralWidget(self.centralwidget)
        self.menubar = QtWidgets.QMenuBar(MainWindow)
        self.menubar.setGeometry(QtCore.QRect(0, 0, 1006, 21))
        self.menubar.setObjectName("menubar")

        MainWindow.setMenuBar(self.menubar)
        self.statusbar = QtWidgets.QStatusBar(MainWindow)
        self.statusbar.setObjectName("statusbar")
        MainWindow.setStatusBar(self.statusbar)

        self.retranslateUi(MainWindow)
        QtCore.QMetaObject.connectSlotsByName(MainWindow)

        self.infoBtn.clicked.connect(partial(self.show_popup))
        self.dateBtn.clicked.connect(self.openDateWindow)
        self.startBtn.clicked.connect(self.openDriveWindow)
        self.contactsBtn.clicked.connect(self.openContactWindow)

    def retranslateUi(self, MainWindow):
        _translate = QtCore.QCoreApplication.translate
        MainWindow.setWindowTitle(_translate("MainWindow", "MainWindow"))
        self.infoBtn.setText(_translate("MainWindow", "About"))
        self.startBtn.setText(_translate("MainWindow", "Driving Mode"))

    def show_popup(self):
        msg = QMessageBox()
        msg.setWindowTitle('About Us')
        msg.setText('Testing')
        msg.setIcon(QMessageBox.Information)
        x = msg.exec_()

    def openDateWindow(self, MainWindow):
        self.window = QtWidgets.QMainWindow()
        self.ui = Ui_DateWindow()
        self.ui.setupUi(self.window, MainWindow)
        self.window.show()
        MainWindow.hide()

    def openDriveWindow(self, MainWindow):
        self.window = QtWidgets.QMainWindow()
        self.ui = Ui_DriveWindow()
        self.ui.setupUi(self.window, MainWindow)
        self.window.show()
        MainWindow.hide()

    def openContactWindow(self, MainWindow):
        self.window = QtWidgets.QMainWindow()
        self.ui = Ui_ContactWindow()
        self.ui.setupUi(self.window, MainWindow)
        self.window.show()
        MainWindow.hide()

app = QApplication(sys.argv)
splash = SplashScreen()
#splash.show()

sys.exit(app.exec_())