This is a factual question although I have not been able to find the answer on Google, but it has an obvious political implication. Trump’s grandfather emigrated to the US in 1885.
Incidentally, I have no idea if my grandparents, immigrants all, ever naturalized. I can’t imagine it would have seemed very important in those days.
Here is a pdf from the Washington Post website that includes an application for a passport made by Fred Trump in 1904 in which he states that he is a naturalized citizen since 1892: https://www.washingtonpost.com/wp-stat/graphics/politics/trump-archive/docs/friedrich-trump-naturalization.pdf
Is there documentation for his assertion, though? Things were squishier back then. My grandfather immigrated around then. We thought he was born in the US. He had a US birth certificate. But after his death, we found that he also had a Russian birth certificate.
I don’t know, but as I understand it, at that time it wasn’t particularly difficult for an immigrant living in the US to get naturalised. So possibly Fred Trump would not have had a reason to lie about it.
According to Wikipdia:
Born and raised in Kallstadt, in what was then the Kingdom of Bavaria, Trump immigrated to the United States in 1885. In 1891, he began speculating in real estate in Seattle. During the Klondike Gold Rush, he moved to the Yukon, Canada and made his fortune by operating a restaurant and a brothel for miners in Whitehorse.[2][3]
In 1901, Trump returned to Kallstadt and married Elisabeth Christ. As he had failed to complete mandatory military service and notify the authorities of his departure in 1885, the Bavarian government stripped him of his citizenship in 1905 and ordered him to leave. Consequently, he returned to the United States with his family.
So he had enough time to be naturalized, but may have lied because he lost his Bavarian citizenship.