>>57873552I did this question many times, but I'll pick his second "first" Pokémon.
David just arrived to Vermillion City by boat. There he went to meet Lt. Surge. They both had a talk, and being "brothers in arms" (they obviously weren't in the same unit, but army men have camaradie with fellow soldiers who served), he made him a favor.
He called up a friend that could give him a lift to Pallet Town. Turns out that friend was Leaf. She took him there with her bike, and during the trip they spoke to each other.
Leaf became a wandering trainer after her League Challenge, and she was helping out proffesor Oak. David admitted that he was travelling because he needed to discover more about the union between pokémon and humans. They hit it off very well, so she gave him a Bulbasaur saying, and I quote, "let's see you handle that, Hoenn Boy."
In Pallet Town, he went to proffesor Oak's lab where, to his surprise, was under Blue Oak's control. Turns out the original proffesor was preparing himself to retire, and Blue chose to take over his stead. A talk later, David needed to register himself as a Kanto Trainer, but he couldn't use the Bulbasaur Leaf gave him. Turns out she does that a lot, and that gives the Pokémon League Association a bit of a problem with Trainer IDs.
David went to pick his new "first" pokémon, and it turned out to be an Eevee. Blue had many of those.
So yeah: unnoficially, his first pokémon in Kanto is Bulbasaur, but officially is an Eevee.