And either player can initiate it at any time. There's no need to use Force or anything to start the race, but it is an action so you must declare it. If you wait till your control phase, and then want to kick start your race, you will use up your action doing it. This means that Light Side gets the next action, from where they will draw their race destiny. So as Dark Side, get it out of the way early, or just ensure you do not initiate it during your own control phase.
Dark side has one other problem if they are trying to maximize their podracing theme.
Trying to get utmost use from Watto's Box . Advisor-ing for it first turn, or drawing it in your opening hand. If you are Light Side, there is not really a best time to start racing, unless your strategy depends upon it. Best for you is to hope that Dark Side falls into the trap detailed above. Drawing Race Destiny Pretty simple on the outside, but in reality there are a few choices available to you.