I'm pretty sure the first birds I ever technically "saw" were House Finches. My first list I ever put on eBird was a whale watching cruise and that included Pigeon Guillemots, Rhinoceros Auklets and stuff so that doesn't really count.
I remember American Pelicans flying over the house, and a Peregrine Falcon which I'm still not sure was an actual Peregrine or not... if my memory from when I was like 6 is any good it definitely was, but who knows!