The Infamous Cruelclaw

Menace
Whenever The Infamous Cruelclaw deals combat damage to a player, exile cards from the top of your library until you exile a nonland card. You may cast that card by discarding a card rather than paying its mana cost.

Bloomburrow

Bloomburrow Promos

If the spell you cast has {X} in its mana cost, you must choose 0 as the value of X.

If you choose not to cast the exiled card, it remains in exile.

Since you are using an alternative cost to cast the spell, you can’t pay any other alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, you must pay those.

You cast the exiled card while the ability is resolving and still on the stack. You can’t wait to cast it later in the turn. Timing restrictions based on the card’s type are ignored.