I assume you will be camping out a night or two including your night at Trail Camp. That will help with your altitude adjustment. If you get to spend two nights before the summit bid that will really help.
From trail camp to the top of the 97 switchbacks can be a rough two hours. From trail crest to the top is another casual 75 - 90 minutes or so. That seems to add up to 3.5 - 4 hours or so, if you keep a steady pace.
Consider how strong you feel getting to trail camp. If you feel strong, leave at 2:15 am and keep a good pace, with some "short" breaks.
If you want a little extra time, leave @ 1:45 am.
If you feel wiped out by your trip to trail camp, leave at 1:00 am. But to me, that seems like plenty of time and some to spare, perhaps arriving at the top up to 90 minutes before sunrise.
If you do get to the top a little early, rest inside the cabin, where it will be warmer and out of the wind. Sunrise is spectacular and worth it. You may even be alone up there that time of day.