There was actually an official Thunderbirds tabletop RPG a few years back, though it was oddly packaged – it was basically sold as an add-on to the Thunderbirds board game – and it’s since gone out of print. Something to keep an eye out for on the used market, perhaps.

As for stuff that’s actually available to purchase, if you don’t mind Fate Core derivatives, you might consider the Atomic Robo RPG. Out of the box it’s a tiny bit more gonzo than Thunderbirds, but not hugely so – it wouldn’t be too much effort to rein it in a little, and the whole “action scientists” conceit that puts as much mechanical weight on brainstorming to figure out what the heck is going on as it does to punching baddies is a good fit for the source material. The big potential hitch is that Fate Core handles vehicles very abstractly, while they’re pretty central to your premise; if you want well-differentiated vehicle stats, you may need to do some tinkering, probably by adopting some of the relevant suggestions from either the core rulebook or the SRD.