If you have already gotten through character select once, the option will be presented, yes.

Aaah, I see what the issue is. I'll take this as an opportunity to redo the prologue skip screen entirely, actually. To both make it look better and also because having the choices be tailored to the last playthrough you did was, in retrospect, a terrible idea. If you played Jun's route, finished it and now want to play Keisuke's, you probably don't want the game to act like you chose to spend time with Jun every time.