For that to happen it would either have to be an activated ability (like its counterpart Glory) or say "At the beginning of your upkeep, if Genesis is in your graveyard, you may pay
{G} any number of times. For each
{G} you paid in this way, return target creature in your graveyard to your hand."
Also note that you have to choose your target at the time Genesis' ability goes on the stack, before you have a chance to do anything else. So you cannot put the trigger on the stack, then discard something to Wild Mongrel and return it; you would have had to discard on your opponent's turn. This is another common Genesis mistake.
