Answer is very simple but many would not accept it because it is not something they like to see or hear. If you (or anyone else) believe that salvation was only through Jesus (pbuh) then you are spot on in thinking and mentioning what you did. However as a Muslim we believe that first human on this planet was Adam (pbuh) and he was also a prophet and therefore prophets have always been there. Muslims believe that there were roughly 124K messengers and prophets first being Adam (pbuh) and last being Muhammad (pbuh). Only difference is that the message given to all of the Prophets before Muhammad was just for that time. For that very reason you will not find any book or original message or teachings from those messengers. Now to answer your question, anyone who believed and acted upon the teachings of any of those the prophets during their time will have so called salvation as all of those prophets gave exactly the same BASIC message about worshiping only one God. Therefore it does not matter when you were born.