Another citizenship by descent question!

This one is tricky though, so if anyone has an in and out knowledge of this, it would be helpful!! I’ll just start with it’s kind of a stretch already since it’s my third great grandparents, who immigrated in 1857 but weren’t naturalized until some years later, and I believe my great great grandma was born before they were naturalized. I can follow that line of thought through if needed but the other big issue, this was on my father’s side of the family but apparently they never actually married…and he’s not on my birth certificate. I know for a fact he’s my father so there’s no question there haha but does that also make this impossible? Thanks for anyones input! I lived in German for three years and would love to go back if possible.

Here’s my descent as I know it:

3rd great grandma: born 1840 in garnsbach, Baden 3rd great grandfather: born 1833 in muhlhausen, waldeck Immigrated : 1857 Naturalized: I’m not sure yet, sometime between 1900 and 1910

2d great grandmother: born in Texas 1859

Great grandmother: born in Texas 1898

Grandmother: born in Texas 1937

Father: born in California 1966

Me: born in Texas 1990