A permanent card is an artifact, creature, enchantment, land, or planeswalker card.

If the player chooses to put a double-faced card onto the battlefield, it enters with its front face up. They may do this only if the front face of the card is a permanent card.

If the artifact, creature, or enchantment is an illegal target as Divine Gambit tries to resolve, Divine Gambit won't resolve and none of its effects will happen. No player will put any cards onto the battlefield.