Can you cast an adventure card from exile after its adventure spell resolves?

When you cast the adventure half of an adventure card, it functions as a spell on the stack. When that spell resolves, instead of going to the graveyard, the card is exiled face-up. This is a special rule specific to adventure cards (CR 715.3).

Once the card is exiled in this way, you gain the ability to cast it as a creature spell from exile. There is no specific time limit imposed by the rules — you may cast the creature half at any time you could normally cast a creature spell, following standard timing rules (CR 715.4).

This is a key design feature of adventure cards: the adventure acts as a 'detour' that temporarily parks the card in exile, giving you the option to deploy the creature on a future turn when it is more advantageous to do so.

Example: You cast Bonecrusher Giant's adventure spell, Stomp, targeting an opponent's creature. Stomp resolves, dealing 2 damage. Bonecrusher Giant is then exiled face-up. On your next main phase, you may cast Bonecrusher Giant as a 4/3 creature from exile by paying its mana cost.

Note: Only the specific exile caused by the adventure's resolution grants this permission. If an adventure card ends up in exile by any other means (e.g., exiled by an opponent's effect), you do NOT get to cast the creature from exile unless another effect explicitly allows it (CR 715.4).