Can I start my game later than the time I set?

Yes, you can start later than the time you set. Playbox does not block a late start, and matches are not cut off at the end time of the game. The start and end time are information for players and for your pitch booking; the real limit is how long you rented the pitch.

Playbox only closes a game that was left open. The deadline is the game duration counted from the last activity: the start time of the game or the start or end of the latest match, whichever is later. Every match you start or finish moves that deadline forward, so starting late and playing past the end time you set is fine; there is no rule to finish by the end time. So you can train for 40 minutes and then play with stats. Up to 30 minutes before the deadline you get a warning. Tell players the real kickoff time in the game chat.