This is a world building exercise, yes...? You fundamentally can't.

Say I hold in my hand a shiny new pound coin I'm about to flip and that Iwager you, if you can call the outcome correctly, you win the coin.

I flip the coin, you call HEADS - Oh, jolly bad luck, its TAILS.

Fortunately for you I'm a time traveler and so I offer you the use of my time machine, thus giving you the opportunity to pop back a few seconds and use your knowledge as someone from the future to guess the outcome correctly.

You pop back in time, after I flip the coin this time (from your persepectve) you call TAILS - TAILS it is, hearty congratulations!

One question - do you win the coin because of your knowledge of the "future" or, do you win it through just blind, random luck, sam eas if you never traveled back through time at all...?

Obviously, in order for you to use time travel to cheat, you'd have to pop back in time considerably further than just a few seconds. In order to impersonate your "past self" you'd have to intercept your "past self" before even meeting me.

Given one's perspective as a time traveler you might call that a "change" to past events or else call it a Predetermination Paradox...

Fancy though the lable may be, does it inform you whether you call the outcome correctly through your knowlegde of the "future" or is it just blind random luck?

From a point of view where time travel doesn't exist, the "past" as we view it is fixed - however, if you could physically travel to (whatever) point in the "past" (from your perspective) the instant you arrive the reality you exist in is no longer fixed: normal physical laws apply - up still remains up, down remains down and the outcome of a coin coming down one side over the other remains 50/50 with a miniscule possibility of it landing on its edge.

Those odds never change, it doesn't matter where you are in time or when, from your frame of reference.

Thus, if you were to travel back in time this way to be physically present to witness past events as they unfold - such as the outcome of a coin flip, for example - you basically have no way to determine whether your ability to call the outcome correctly is because of your so-called knowledge of "future" events or whether or whether its just down to blind random luck, same as if you never stepped into a time machine.

If you can be physically present at some point in "the past" - from your point of reference - so too can some other time traveler, including yourself - you literally have no way of determining whether where you are is the "actual" past as it actually happened, or some close parallel either created by by yourself or some other time traveler deliberately or else as a means to ensure the correctr sequence of events happens in order to ensure they can return to whatever point in time and space they originated from.

Best you ever get is a close parallel - there's no physical way of determining which, other than steering the hell away from time travel.

Unfortunately - personal abstinence doesn't guarantee so other time traveler showed up, either advertantly or else otherwise inadvertently creating the reality in which you currently exist....

And all that's just over a simple coin toss.

You can't predict with any accuracy events as they happened in your original timeline will happen in the "past" unless you your elf become instrumental in their coming about.

In which case. again - if you can be physically present in the past in order to whiteness history as it's supposed to have unfurled - so to can some other dick with a time machine, including you.

Do you see the inherent problem?

Everything comes down to whether time is Linear (The Block Universe) or Branching (Many-Worlds interpretation) - and neither give you the tools unnecessarily to determine which, not even time travel itself.

Thus, you have no way to prove anything about your time travel status - unless you yourself personally engineer events to unfold in the way your version of history suggests they do.

Its kind of a thing with history. History as its taught isn't fact so much as a consensus of opinion based on whatever evidence supporting whatever mechanic exists - even through your own life time, the interpretation of how specific historical events actually took place changes, the more new evidence concerning them emerges to support whatever consensus.

History in the broad strokes remains untouched - Hitler annexe's Poland 16 days before the Soviets annex the Baltic States in most timelines your ever going to encounter, but the specific mechanics of those events changes over time as more evidence to support one interpretation emerges over whatever currently existing one.

In short - you can't use time travel or knowledge of "the future" to accurately predict the mechanics of specific historical events, only history in its broadest strokes: like calling the outcome of a coin toss correctly, you don't know why your right, only that that's what happened and have no actual clue what the actual mechanics governing that outcome were.