The best thing you can do is get a 15-20 min warmup in. Your races are short, but they can be less painful if you are properly warmed up.
Second, don’t start off too hard in the opening sprint/lap. Go at a pace, for that first lap, that seems slightly easier than what you think you should be doing. 15 minutes into the race, your legs will be thanking you.
Last - hold those handlebars (hoods are my preferred steering point) as loosely as you can while maintaining control. If you do a death grip, your hands will be cramping by the end of the race.