If you'd rather just watch a video tutorial on how to do this, I have one here:
Ok, so if you have no idea what I mean by "start boosting", first go and watch any video of someone speedrunning an individual level. If you were left in awe at how they were able to instantly start the race at full boost speed, you're not alone. Few people know of this trick, and even fewer could actually pull it off. That time has passed. After some thorough experimentation and some healthy boredom, I'm pleased to present to you the full guide about start boosting, henceforth known as "snap boosting" (that's just my name for it.)
To start, what is a snap boost? A snap boost is when, through a certain series of button presses and specific timing, you can instantly go from a dead stop (or extremely low speed) to a full boost (just shy of 300mp/h). What makes this different from any other boost is that it doesn't require hitting a boost strip OR using the Turbo weapon. It's all done with just a few well-timed button presses.
Before you get bored by any technical details, I'll tell you how to do it. There are actually two different-ish methods of performing a snap boost, but they both work on the same principle and basically use the same button presses and timing. The only difference is that one is done at the very start of a race, and one is done at any other time. Since most people are only familiar (and interested) with snap boosting at the beginning of a race, I'll explain that method first.
---------------------TUTORIAL STARTS HERE----------------------
To start, once the race start music starts (before the stop/go lights start the countdown), press and hold R. The timing here doesn't matter much, so long as you just start with R before the next step. Next, just BEFORE the transition between the top light and the next light (to within about 1/6 of a second), press and hold A while still holding R. Keep holding both buttons until the final light turns on and the race starts. As soon as the race begins, let go of R while still holding onto A. If you're suddenly going roughly 294mp/h out of nowhere, then congratulations!! You've just performed a snap boost!
The simple and short explanation is just to start by holding R, then press and hold A just a couple frames before the first light turns into the second, then let go of R as soon as the race begins. Luckily, you have at least 3 or 4 frames of leeway on the timing here. When you press A, you'll want to press early rather than late, as a late timing will more than likely kill the snap boost entirely, while and early timing will give you what I like to call a "half snap", where you get a moderate boost akin to just going at a normal, non-boosted top speed. When you let go of R just as the race starts, you'll want to press it later, rather than earlier. Too early will cause your RPMs to quickly go the wrong way, and physically shifting from a reverse direction to a forward one is what triggers the snap boost. Releasing R late will just delay the snap boost by a few frames, which just shaves a small fraction of time from your run. You'll still boost at full speed if you're just a few frames late.
If you want to snap boost at any other time BESIDES the very start of a race, the procedure is basically the same, minus one little part. You'll need your tachometer (RPM gauge) visible for this method. Come to a dead stop and, like before, hold R. Instead of waiting on a light, just start holding A as well. Now, instead of releasing R when the race starts, you'll let go of R right as you hit 3100RPM, give or take about 100 (preferably later rather than earlier). If done correctly, you'll snap boost in the same way that you did using the start-of-race method. The timings are exactly the same, but the only difference is that one method uses the lights as a reference point so you can time it perfectly, while the other just relies on watching the gauge for the same timing.
-------TUTORIAL ENDS, BEGIN BORING PART HERE-------
So, with the tutorial and tips out of the way, here comes some more nitty-gritty info I've gathered from plenty of observation and trial-and-error. The actual trigger for the snap boost is being in reverse, in first gear, while going roughly 3100RPM (roughly 3000-3200RPM or so), then letting go of R, thus taking you out of reverse. For whatever reason, shifting from first gear in reverse to forward while going roughly 3100RPM creates a snap-boost. I'd love to give some technical explanation about some kind of integer overflow or quirk in the gear ratio calculations or something, but I have nothing. I know HOW it works, not why it works (from a code standpoint, at least).
The snap boost actually has a few limitations and quirks. In time trial mode, the snap boost works at its best, and is the easiest to work with. In the normal Grand Prix mode where you race other cars, we run into some problems. See, there's something of a safety mechanism built into GP mode that prevents us from actually snap boosting at the start of a race. My personal guess is that the developers found out about the snap boost during development, but decided to add a cheap workaround to it instead of actually fixing the glitch. Basically, until you've crossed the start/finish line, the game can consider you as being on lap 0. Once you've crossed the start/finish line after a race starts, you're technically on lap 1. Until you're on lap 1, the snap boost WILL NOT WORK. It just doesn't. If you're on lap 1 AND remain forward of the start/finish line during the entirety of the snap boost process, it'll work. If your car is on lap 0, even if you just entered lap 1 and reversed into lap 0, snap boosting doesn't work. TL;DR, you can't snap boost at the start of a GP race. If you really wanted to, you could get a little bit in front of the start line (putting you on lap 1) and THEN snap boost (assuming you never cross into lap 0 during the process), but by this point the other cars have built up enough momentum that you'd have been better off just starting as normal.
While your GP starts are doomed to a normal and typical non snap boosted start, you can still benefit from it just a tiny bit. I've found that even though starting a GP race with a snap boost doesn't work, it will still start you out about as fast as if you were to normally pre-rev your engine. In fact, it's just a tiny bit better to do one of these failed snap boosts as opposed to doing it the normal way. On the top-class engines, I've found that you'll be about 10mp/h faster by the time you cross the start line if you snap boost instead of doing it the normal way.
You'll still have an opportunity to snap boost for real during a GP race. The only practical time to use it is if you've been hit by an attack or go out of bounds and are somehow left at 0mp/h. Normally, it sucks when this happens since you have to waste time getting back up to speed, but you could instead just snap boost and get back to full speed in much less time.
Oh, the other thing to note is that snap boosting sometimes doesn't work so well when you're on an incline. The key word is "sometimes". My guess is that the incline makes you speed up either too quickly or slowly, thus making the boost less consistent.
As far as I can tell, snap boosting works on all engine/car types, regardless of item configuration. This also works in GP on any class, assuming you snap boost after having crossed the start line.
...aaaaAAAND, that's it! That's basically everything there is to know about snap boosting...unless I just forgot about something, in which case I'll update this as necessary. Good luck to all of you hopeful speedrunners out there. I hope this guide helps you break those records!