Do adventure cards have summoning sickness?
302.6. A creature’s activated ability with the tap symbol or the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. A creature can’t attack unless it has been under its controller’s control continuously since their most recent turn began. This rule is informally called the “summoning sickness” rule.
The rule covering what happens when you cast an Adventure:
715.3d Instead of putting a spell that was cast as an Adventure into its owner’s graveyard as it resolves, its controller exiles it. For as long as that card remains exiled, that player may cast it. It can’t be cast as an Adventure this way, although other effects that allow a player to cast it may allow a player to cast it as an Adventure.
I'm assuming the possible confusion here is about what happens if the card has been in exile since your turn began. This makes no difference. The card is not a creature unless it is on the battlefield (instead, it is a creature card), and so it will still have summoning sickness even if you cast it from exile multiple turns after the Adventure resolves.