Does an annulment mean that my marriage "never existed"?

No. Obviously the couple was wed according to civil law and lived together, and possibly had children. They have a "history" from being together. It is presumed that both parties entered the marriage with good intentions. No one can deny that a relationship existed in some fashion, at least for a time, with its own joys and sorrows, its own hopes and disappointments. Good and bad memories will always remain. In almost all cases, a civilly recognized union was at least certainly present.