If you put a permanent with a kicker ability onto the battlefield without casting it, you can't kick it.

If a spell's kicker cost was paid, the spell is "kicked."

The kicker ability doesn't let you pay a kicker cost more than once.

To determine a spell's total cost, start with the mana cost (or an alternative cost if another card's effect allows you to pay one instead), add any cost increases (such as kicker), then apply any cost reductions. The spell's mana value remains unchanged, no matter what the total cost to cast it was.

If you copy a kicked spell on the stack, the copy is also kicked. If the copied spell is a permanent spell, the token the copy of that spell becomes when it enters is also kicked.

If a card or token enters as a copy of a permanent, the new permanent isn't kicked, even if the original was.

If the target creature card is an illegal target as Sheoldred's Restoration tries to resolve (usually because the card has been removed from the graveyard in response), it won't do anything. You won't gain or lose life, and Sheoldred's Restoration will go to the graveyard rather than be exiled by its last ability.