Under [Game Menu > Settings > Advanced Settings] try switching controller type to joystick.
(You can switch controller type back and forth between joystick and keyboard without exiting a game if need be.)
Then when you need to get past an intro screen in a game press X on your controller. (or whichever button you have mapped as X(it’s the square on sony controllers)) The vice core’s virtual keyboard comes up, but isn’t very functional without a mouse but that doesn’t matter since we are now past the intro screen and can just hit X again to hide the virtual keyboard.
This got me past the intro screen on multiple games that I tried.
While not a complete solution, it hopefully can get you playing your games.