No
It started with one of Obama’s state legislative race opponents, Andy Martin in 2004.
https://www.politico.com/story/2016/09/birther-movement-founder-trump-clinton-228304
Personally, I think Obama himself was saying he was born in Kenya while a student at Harvard for one reason or another. (To make himself seem more “exotic to stupid White coal burners perhaps.)
Early on his first publicist put out a printed blurb on him saying he was born in Kenya as well
You know why don’t you? Being an African was a lot better than being a plain old run-of-the-mill American Negro. I mean, suppose you got a disease that turned you physically into a Negro. Your hair darkened and your hair kinked up. Now would you change your name to Travonicus T. Washington, from Alabammy, or Mogombe Smith from The Gambia??? You know, being African is not just more exotic, it is a lot more practical too, because Africans fit in better than Negroes, and have better job chances.
Having seen this in action, claiming to be an African from Africa gets you a lot more company in bed. An Obama seems like one of those people who had a revolving door on his bedroom.
Either way The Birther Movement began with Democrats not Republicans.