lbxProgramme.SelectedIndex = 3;
lbxProgramme.ScrollIntoView(Listbox.SelectedItem);

void TestPage_Loaded(object sender, RoutedEventArgs e)
{
    lbxProgramme.Focus();
    FinishedLoading = true;
    JustLoaded = true;
    lbxProgramme.SelectedIndex = 3;
}

void lbxProgramme_SelectionChanged(object sender, SelectionChangedEventArgs e)
{
     if (JustLoaded)
     {
        JustLoaded = false; // set to false so we don't keep executing the next line
        lbxProgramme.ScrollIntoView(lbxProgramme.SelectedItem);
     }
}