Bzzt! Wrong! Spectacularly wrong, in fact, since the Spanish forced all Jews to convert, and practicing Judaism anywhere in Spanish territory could get you burned at the stake as an apostate. Sure, many were still practicing in secret, but not in their own, dedicated synagogues. When Britain in Spain got into a war with Spain in 1739 and Spanish troops landed in Georgia, the Jewish community there--most of them refugees from the Spanish empire-- fled in terrror from the Inquisition they knew would follow the Spanish soldiers.
No, the first purpose-built synagogue anywhere in what is now US territory, Shearith Isreal, was dedicated in 1730 in New York City. The oldest synagogue still standing is located in Newport, RI--the Touro Synagogue, dedicated in 1763.
Don’t try to confuse our friend with the truth, he has his own sources which cannot be verified via the internet or the public library’s.