No, it's not like that: generate a random Bitcoin address and it's practically guaranteed that it will be empty. But in this case, if the time traveler picks a

No, it's not like that: generate a random Bitcoin address and it's practically guaranteed that it will be empty. But in this case, if the time traveler picks a random key for their secret, it's equally likely that it gets brute forced on the first attempt as it is the trillionth attempt. There's no statistical guarantee except that on average it will take a certain number of attempts.