Look at how many heats you may be doing. Also see if it's an "all category" or if it's broken down. Check also if you can draft or not ("lanes").
If it's all category there will be guys that can go from the gun.
Although technically warming up should be good, I found I can make these efforts without much of a warm up (I got that tip from football players who said they did their best maximal bench presses cold). I also found that after 3-4 my top end drops dramatically.
If it's truly 1/4 mi (400m, give or take), with a rolling start (implies they won't have people to hold up starters), with lanes, it's going to be really, really, really hard. Time trial at 300%-350% FTP, with a 500%-600% start effort.
If it's shorter (one of the street sprints I did ended up closer to 125 meters), with holders (that got rounded up last second - they were other racers), then it's a different thing altogether.
If there's a slight crosswind you can draft even with lanes. See if there's a way to get into the protected lane.
If it's bracket (and not track type bracket) if you lose you're out, so every race should be do or die at the line. If it's track bracket and you lined up against a pro that won a $50k national one mile "shoot out" (beating, among others, Marty Nothstein), then you save your legs for the repechage.
Unfortunately I was in a regular bracket race when I ran up against the pro. He was kind enough to keep me about 3' off his front wheel. He made me look good while he annihilated me.
(If you don't know what a repechage is, read the rulebook at usacycling.org - link on left side).
Whatever you do, practice making shifts under full load, like 100% full load.
If it's a rolling start don't start in a big-big. Also don't back pedal when you're waiting. You shouldn't anyway but if you backpedal in a big-big or big-second-biggest then you'll derail your chain. For rolling start I'd look at a 53x19 or so to start, maybe a 21 if it's actually 100-150 meters. You'll be finishing spinning a 14 or slogging a 12. If you're good you'll be spinning the 12.
Absolute lightest wheels possible. Top end is important, yes, but you'll use a lot of gas getting the bike going. Ultimately light aero would be great (carbon tubulars). It's easy to accelerate light wheels quickly over and over. It's hard to wind up heavier aero wheels to an insane top speed over and over. By the 3rd round the fastest speeds will be lower; light wheels should trump aero wheels.
This is assuming that there are no 1s or 2s in there, guys that will be able to go fast on their light aero wheels every single time.
Time doesn't matter as much as beating the others. I understand it's good to see where you sit vs the competition. You want to accelerate towards the line. If it's really 400m, you should be hitting 40-42 mph minimum. If it's 150m, 40 mph. If you're allowed to draft, 42-44 mph should keep you up there.
If you're stuck in the 30s then view this year as practice for next year.
Inevitably there are riders who truly believe a fixed gear track bike works best. Granted, there are no gears. But over even 100-150 meters, the guy with gears will have an advantage, even over the biggest, baddest track rider. The aforementioned $50k one mile sprint pro (his take was $10k of the $50k), he destroyed a super strong trackie in the final sprint. Just annihilated him. I wanted the $50k sprinter to win but I didn't think he could beat the trackie. Trackie ended up shooting himself in the foot - he went so hard in the early rounds to eliminate competition that he was getting tired by the end. Remember, fixies can't coast - if you have a huge margin, you're still pedaling etc. And it's hard to adjust gear for changing conditions or for gusty winds.
good luck
cdr