Pretty sure it's turn 7.
You will always have $2 because you have at most 3 Estates/Shelters and all your treasures give $1. On the second shuffle of the game after turn 4, your deck has 4 Fool's Gold in 14 cards. You'll draw 3 hands this shuffle, so one of those hands must have 2 Fool's Golds. (It doesn't matter whether FG misses the reshuffle or not.) The worst case is the last hand of the 3rd shuffle which is turn 7.