Having a "Command" and being in temporary command on a ship or a landing party are two different things.How would it work, the shuttle mission being Spock's "first command"? We'd both have to narrow down the definition and make assumptions about Spock. But both are certainly doable.
To get a "Command", a Command-level Officer of at least Captain (Kirk) assigns a ship (shuttlecraft) and crew (six other personnel) to an officer (Spock) for independent action (in this case, explore the nebula) away from the command authority (Kirk on the Enterprise). That officer (Spock) is solely responsible for the ship, crew, and success of the mission.
In contrast, Spock being in temporary command of the Enterprise while Captain Kirk is on a planet or another ship is not a Command. The Enterprise was not assigned to him by a Command-level Officer. The highest ranking officer can take Command of a ship if he (and the command crew) of the ship can officially prove that the Captain is dead or unable to continue command of the ship (comma, insane, too old, etc.).
Technically, Spock was in fake-Command of the Enterprise in The Menagerie when he faked Kirk's orders that Spock was in Command. This Command came first if you use Broadcast Order, but second if you use Production Order, but in that case, it was fake so it shouldn't count. Up until that point, we don't see Spock with a Command until The Galileo Seven.