Can you activate a crew ability on a Vehicle the same turn the Vehicle enters the battlefield?

Crew is an activated ability written as "Crew N" on a Vehicle artifact card. Activated abilities can be activated at any time their conditions are met unless a rule or the ability itself says otherwise (CR 602.1). Nothing in the Crew rules (CR 702.122) restricts activation based on how long the Vehicle has been on the battlefield.

The summoning sickness rule (CR 302.6) only prevents a creature from attacking or using activated abilities with the tap or untap symbol in their cost. A Vehicle sitting on the battlefield is an artifact, not a creature, so CR 302.6 doesn't apply to the Vehicle itself. The creatures you tap to crew it are subject to summoning sickness in the normal way — you cannot tap a creature to crew if that creature entered the battlefield this turn and hasn't had haste (CR 302.6).

So the key distinction is: the Vehicle can be crewed the turn it enters, but the creatures doing the crewing must have been under your control since the beginning of your turn (or have haste) in order to be tapped for the crew cost.

Example: You play Smuggler's Copter on your main phase. You also control a Llanowar Elves that entered the battlefield on a previous turn. You immediately activate Crew 1 by tapping the Elves. Smuggler's Copter becomes a creature this turn and can attack — no problem. However, if the Elves had also just entered the battlefield this turn without haste, you could not tap them to pay the crew cost.