The answer is: it depends. Is it possible you will get to the Schengen on the 24th? Let me give you two examples.
I will pretend you are flying from Mexico City to Frankfurt.
If you have a direct flight? That leaves Mexico City at 8:50PM and that's already 3:50AM next day in Frankfurt. So by Frankfurt time it is already the 25th. In this case you will be allowed to board because there's no way to get there before the 25th. This is true for almost all transatlantic flights to Schengen from America.
But let's say you are leaving on the 23rd arriving to London on the 24th where you have a long, overnight layover and then board a flight to Frankfurt. Most likely you will not allowed to board because it's possible you will be rescheduled on a different route/schedule which might get you to Frankfurt on the 24th. Of course, it's also possible you can work with the airline to reschedule you in such a way that you only get to Schengen on the 25th. But there is always a possibility of diversion, emergencies and whatnot and the airline most likely won't take the risk -- it's a significant financial risk to transport someone whom they know will be turned back.
So: it depends.
And no, if you land at 24th 11:30pm you will still not be allowed, you can't linger in the restroom for half an hour, this is not allowed.