It's not annoying, really. I just hasn't summarized your suggestions yet because I was engaged in making a splash screen and music for the demo, but I keep it mind. You can see the updated version of this demo by Wokwi link from the post #1 now. To start the demo you can push select joystick button as xfpd suggected in the post #5.
I have implemented your idea about starting the game like so. Now I need some time to think what may be wrong, what to improve and how to proceed next. Thank you both for your help and advice very much.