This scenario doesn’t specify you go back in time though.

I can't remember what the documentary is called, but there was a recent series about a scam with the old McDonald's Monopoly game. Some guy who worked the game knew the winning numbers and would get them to various friends and distant family members and take a cut of the prize for himself. It turns out that the chance that very distant relatives would both win were incredibly low odds and that sent a lot of red flags to the FBI which led to him being caught.

Anyway, my point is that you really could likely get away with winning one, possibly two of those lotteries before feds come asking you questions lol