Instant gratification makes things tricky.

The problem with a pre-built bike that you will encounter is that you'll very soon see the need for upgrades. Probably instantly.

You'll be standing in the starting blocks and notice the odd feeling of your crank arms actually twisting. In a sprint, you'll feel your wheels, tires, handlebars and stem flexing under the forces you are transmitting through them.

Just like that, you need to buy new parts and just like that, the cost you are now incurring is the same as if you had just bought a frame and built it up as you wanted to. Your junk bin is now just a little bit fuller.

If you want to get on the track immediately, take the racing courses on the track's rental bikes while you build up your own bike. This could only work in your favor, because any experience will give you more insight on what kinds of parts you want and what kind of gearing to run.