Julie, you should be fine changing to synthetic immediately. In fact, all engines are fine to use synthetic from the first startup.
I can assure you that the dealer will probably try to steer you away from synthetic oil, though, as the TSX 'technically' doesn't call for it, they won't often recommend it. However anyone that does their research will see that longer OCI's on a better oil is no worse for a car than shorter OCI's on dino oil.