Activating Golos during another player’s turn
Gatherer often answers rules questions about cards with special effects directly. In this case, it says


  Golos’s last ability doesn’t change when you can play the exiled cards. For example, if you exile a sorcery card, you can cast it only during your main phase when the stack is empty. If you exile a land card, you can play it only during your main phase and only if you have an available land play remaining.


Which is to say, if you activate him on your opponent's turn, you can only cast exiled instants and cards with flash, just as with regular cards from your hand.