forcing initial callback despite dash.PreventUpdate preventing it from other function

When a dash app is started, all callbacks should be fired according to the dash documentation. But when callbacks are linked (ones output is the other ones input) the initial callback of the latter is prevented when the first raises a dash.exceptions.PreventUpdate or returns a dash.no_update. Although I can somehow follow that logic, it was not clear for me that this would happen, and I am interested in reading somewhere the reasons behind this, although I have no idea where.

More practical, I would like to fire the initial callback nevertheless, is this possible? The code below is a minimal example of the problem:

import dash
import dash_core_components as dcc
import dash_html_components as html
from dash.dependencies import Input, Output, State
import plotly.graph_objects as go
import numpy as np
from time import sleep

app = dash.Dash(__name__)
app.layout = html.Div([
        html.Button('test', id='button'),
        dcc.Dropdown(id='super', options=[{'label':x, 'value':x} for x in ['test1', 'test2']]),
        dcc.Dropdown(id='under', options=[{'label':x, 'value':x} for x in ['under1', 'under2']]),
        dcc.Graph(id='graph'),
])

@app.callback(
        Output('super', 'value'),
        Input('button', 'n_clicks'),
        prevent_initiall_call=True
)
def set_super_value(nclicks):
    if nclicks is None:
        return dash.no_update
    return 'test2'

@app.callback(
        Output('under', 'value'),
        Input('super', 'value')
)
def set_under_value(val):
    sleep(5)
    return 'under1'
    
@app.callback(
        Output('graph', 'figure'),
        Input('under', 'value'),
)
def make_figure(val):
    sleep(5)
    if val == 'under1':
        return go.Figure(go.Scatter(x=np.arange(0,1000), y=np.sin(np.arange(0,1000)/100)))
    else:
        return go.Figure(go.Scatter(x=np.arange(0,1000), y=np.cos(np.arange(0,1000)/100)))    

if __name__ == '__main__':
    app.run_server(debug=True)

This is the initial state: And this is how I would like it to be:

In this simple example I can always set this initial value as the 'value' option in the initial app.layout variable, but the problem in my actual application makes this a suboptimal solution in my eyes.

* Edits made to the code to make specify the problem a little more specific. Code still works and screenshots still apply (but