Any way to always start full screen?

I don't think there is. Do you really need to automate a single double-click in the game window? Then write a very simple Autoit script to do just that (and maybe automate launching games as well, or whatever your goal is)

https://www.autoitscript.com/autoit3/doc...seMove.htm
https://www.autoitscript.com/autoit3/doc...eClick.htm