In Star Trek: First Contact, the Vulcan who makes first contact with humanity is not Vulcan at all: it is Zefram Cochrane who makes the contact, while the arriving Vulcan is Solkar.
The correct answer to the film’s human inventor question is Zefram Cochrane. He pilots the Phoenix, humanity’s first warp-capable spacecraft, during its historic flight on April 5, 2063. The flight attracts a Vulcan survey ship, whose crew lands after detecting the warp signature.
Solkar is the Vulcan captain who steps out of the ship and greets Cochrane, creating the first official contact between humans and Vulcans. Because the scene includes both characters, their roles are frequently mixed up.
Cochrane is played by James Cromwell in the film. The Phoenix is built from a converted nuclear missile in a missile complex near Bozeman, Montana. The event becomes a foundational moment in Star Trek’s history and is referenced throughout later stories.