How do I make a Powershell WPF form run a function when loaded (and display itself)?

I have a login script in Powershell that I am using a WPF form for. I want it to load a form, and then update the form with the scripts progress.

I am using:

$Window.Add_Loaded({ 
    DoStuff
})

However, what is happening is that the script runs, and then when completed it loads the form.

If I put a button on the form to trigger the script function, the form loads, and then updates as expected, i.e.:

$Button.Add_Click({
    DoStuff
})

A simplified example of this is as follows:

Add-Type -AssemblyName presentationframework

[xml]$xaml = @"
<Window
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    x:Name="Window" Title="Countdown" WindowStartupLocation="CenterScreen" WindowStyle="None" Background="#2C2A6F" ResizeMode="NoResize" Width="100" Height="140">   
        <StackPanel>
            <Label Content="3" x:Name="Counter" HorizontalAlignment="Center" VerticalAlignment="Center" Foreground="White" FontWeight="Bold" FontSize="90" Padding="0,0,0,0" />
            <Button Content="Go" x:Name="Button" />
        </StackPanel>
</Window>
"@ 

$reader=(New-Object System.Xml.XmlNodeReader $xaml)
$Window=[Windows.Markup.XamlReader]::Load( $reader )

$Counter = $Window.FindName("Counter")
$Button = $Window.FindName("Button")

$Button.Add_Click({
    Countdown
})

$Window.Add_Loaded({ 

})

Function Countdown(){

    for($i=3; $i-ge 0; $i--) {
        $Counter.Content = $i
        $Window.Dispatcher.Invoke([Action]{},[Windows.Threading.DispatcherPriority]::ContextIdle);
        Start-sleep -Seconds 1
    }
}

$Window.ShowDialog()

This works, with the form loading, and then when I click the button it counts down to zero. However, if I change it to:

$Window.Add_Loaded({ 
    Countdown
})

The script runs with the form not yet visible, and then displays the counter at zero.

How can I set this so the form is shown, then the function triggered to begin the countdown automatically?