You can write all of the advancements off as luck, inspiration, or drugs and blend in until some brain scanning technology is invented that could find out that

You can write all of the advancements off as luck, inspiration, or drugs and blend in until some brain scanning technology is invented that could find out that you're being disingenuous with high confidence. By then, the idea of time travel might not be that exotic. Maybe you send back a way to fool that technology and then it's a cat/mouse game.