OK, so the information is all here but needs to be peaced together. I suggest a new complete answer, which is:
Left click "app.UIFigure" in the Component Browser (right column) -> "Callbacks" -> "Add startupFcn callback" -> enter the following code:
app.UIFigure.WindowState = 'maximized';
This opens the window in smaller size on startup and subsequently resizes it, adjusting the content appropriately. For the resizing of the contents to really work properly, I higly recommend using an "Auto-Reflow" (i.e. responsive) layout of your app. If you leave out drawnow, the app opens fullscreen right away, but it does not adjust the contents.