The idea that Spock was the first Vulcan in Starfleet seems to be a bit of common cultural knowledge with little or no foundation.
The StarTrek.com biography states;
Because the young Vulcan chose to join Starfleet, he and Sarek opened an 18-year rift over Sarek's hope his son would attend the Vulcan Science Academy. Spock was the first Vulcan to enlist in the Federation Starfleet, serving aboard the U.S.S. Enterprise under Captain Christopher Pike as a lieutenant, and later for James T. Kirk.
But the presence of Admiral Patar in Discovery S02:E09 strongly suggests otherwise. However it is possible that more senior Vulcans transitioned from another service (such as the Vulcan Science Academy) after Spock joined.
T'Pol is another common problem with this, however my understanding at the moment is that Enterprise NX-01 is an Earth Starfleet, not a Federation Starfleet vessel and as such T'Pol, no matter what her status on Enterprise, would never have been a member of "Starfleet", as the organisation in question does not exist until after the end of the series Enterprise.
Is there any canonical data to confirm or categorically disprove the status of Spock as the first Vulcan in (Federation) Starfleet?