Classically, (and with classically distinguishable particles) there is no method. Just like there is no method to prove that the universe is bounded spatially.
If you travel and things look the same, you can't prove they are the same, the universe could just be repetitive spatially and/or temporally.
I know that it is very problematic for the general case (if there are in the Universe?). But when we say a very limited space (eg. in the laboratory), we can prove that there is no CTC in this limited space?
Every experiment and observation has some finite precision. So classically, according to GR, you could have a very tiny spinning black hole that that is so small that the odds of it getting close enough to your detectors to be detected is super small and yet inside it could be a region with time travel. But the time travel region is inside an event horizon, so you wouldn't notice.
The precision issue is like trying to prove the mass of a photon is zero. With a good experiment you can prove that it must be tiny, and with better experiments could prove it must be even more tiny. But you can't prove it is zero.
You can exclude tiny black holes. But there could always be even more tiny ones that weren't ruled out. So whatever precision you have there could be a small enough black holes that aren't ruled out. So no experiment can rule out time travel. So relax, and don't worry about it. If there is time travel but it doesn't affect you, then it's no big deal.