Time Travel PoC?

if time travel exists, nobody outside of the travelers will ever know.

Even if a giant infrastructure of travelers already exists in the present (their past).

If you're looking forward to the coming events, there are thousands of ways for everything to happen. But if you already know how something is going to happen and when, all bets are off, you don't need to hope, you know it.

i.e, you know that the way the bus does, you need to take the bus, but you don't know exactly when the bus will get to where you are - or you will be - waiting for it. But you've got more than enough information to plan ahead, even to do other tasks, before you get to the point of meeting the bus you will ride.

This is how the future known will probably be for a time traveler working in the past, maybe events can change a little here and there (maybe that's possible when you mess with the past), but at some point you know "the bus will be there, not early than X not later than Y" (and you can add geographical coordenates probably, close to military GPS precision).

So trying to nuke the planet or a similar drastic event, even if somehow get to get hidden in the present, will be fully known in the future, specially in the far future (a couple of centuries ahead).

Some stuff will be lost to history, but in this century most probably many data points will be stored and/or re-processed at some point, giving the travelers enough information to know with a high degree of certainty where and when, most probably, you can "take a bus" to get to certain destination.