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“If time travel is possible, where are the tourists from the future?”
― Stephen Hawking, A Brief History of Time
If a time traveler is getting rich off bitcoin then any computer synced up to the blockchain has evidence of time travel. The trick is knowing where to look on the blockchain for the "smoking gun".
The first natural place to look would be bitcoin's "Rich List". Since the blockchain is public it is possible to know how much each address has. A time traveler wanting to profit would go to the beginning (around 2009) and mine a bunch of bitcoins when it was relatively easy for solo miners. Once the time traveler was satisfied by the number of coins mined to the wallet's public address the time traveler could return to the future with the private key. The mined bitcoins would be safely preserved in the blockchain between past and future.
That's a nice thought but one rather large amount in one address would make it too obvious to primitives in the early 21st century like the nerd running satoshinakamotoisatimetraveler.com.