Time Trial events are unique in that the results are stored on FM's server(s).  If you wish to participate in a Time Trial Tournament or Challenge, but don't have a fully-upgraded car, you can upgrade your car temporarily.  First do a cloud save (or backup your profile by other means), then you can spend as much Gold as necessary to upgrade your car, and even skip service times and replenish drive pips.  Once you've run the TT as many times as you wish, you would then restore your backup (from your previous cloud save or external backup) and get all your Gold back.  Your best TT result is still stored on the FM server(s).