How can I fully install a disc game before launching it
Solution 1:
I believe the only way to confirm a game is fully installed is to put the disc in and wait for it to install fully. By which I mean, put the game disc in (but don't start it) and you'll hear the disc start to spin, if it's fully installed, after roughly three minutes you'll hear the disc stop spinning, if it doesn't stop, it's still installing and will stop the disc when it's finished.
Similarly when you first put the disc in it will keep installing from the disc and when it's done will stop the disc which is your cue to know it's done.
That's the only way I've ever been able to tell, the install progress bar is useless because that just tracks the install time of the data required to run the game, not the whole install. The size on disc is equally unhelpful in this regard as each game will reserve space for its full install from the off, even if it's only currently installed a fraction of that.
All that said I've not noticed any particular issues with games only being partially installed and I can't see that extending beyond the first couple of sessions.