Enterprise was a Starfleet ship with an almost entirely human crew running under the aurothity of the UESPA.I pretty much assumed that he was the first 'Human/Vulcan Hybrid' in Star Fleet.
But technically, T'Pol (as far as we know) only ever served on board a Pre-Federation Earth spaceship and Burnham is a Human who lived with Vulcans.
So nothing so far, (that I can remember) has dissuaded me from believing that Spock wasn't the first Vulcan to serve on an actual Federation Star Fleet starship.
Addendum:
I forgot about the USS INTREPID (NCC-1631)...
Completely manned by Vulcans.
Though that set of circumstances could have evolved after Spock joined Star Fleet and went through the academy.
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Intrepid might have had a similar arrangement running under the aurothity of Vulcan Expeditionary Group.
That would imply the Tellarites, Andorians, etc might well have their own ships as well, which is why they aren't often seen.