It doesn't seem likely. Vaccines were mostly rolled out in the west (read: United States), whereas the initial variants (alpha and delta) were a result of COVID

It doesn't seem likely. Vaccines were mostly rolled out in the west (read: United States), whereas the initial variants (alpha and delta) were a result of COVID proliferation in unvaccinated areas. Delta, for example, first really blew up in India. It is important to not forget the little details, and to avoid speculations based on broad statements (e.g. the vaccines "rolled out" and we got "more variants"). The vaccines started rolling out to very specific locations and we got variants everywhere.