Hm, not really. That would make you a second-generation immigrant. [1]
First-generation immigrants are folks who are born outside the US and naturalize. "In the United States, among demographers and other social scientists, 'second generation [immigrants]' refers to the U.S.-born children of foreign-born parents."
Not in the strictest sense, but it's not the bright line you're making it out to be either.
Unless your ancestors were in the Americas before Columbus arrived, you're an immigrant. First generation, tenth generation, a hundred generations from now, it doesn't matter. Your great great grandfather landed at Plymouth Rock? You're not native.
First-generation immigrants are folks who are born outside the US and naturalize. "In the United States, among demographers and other social scientists, 'second generation [immigrants]' refers to the U.S.-born children of foreign-born parents."
Not in the strictest sense, but it's not the bright line you're making it out to be either.
[1] https://en.wikipedia.org/wiki/Immigrant_generations