The Constitution was signed in September 1987, so no.
“The Constitution was signed in September 1987, so no.”
Assuming you meant 1787, well, yes, but it wasn’t ratified until June of ‘88. The 1st Congress didn’t meet until March of ‘89, passing the Naturalization Act one year later, in March of ‘90. That leaves a window of two years between the existence of the U.S. and the act, which hardly counts as not having “a naturalization process back then.”
Do you honestly think they couldn’t have had naturalized citizens in mind for the Senate because there wasn’t a naturalization act until one measly year after Congress first met?