Did Jesus exist before he was born?

A continual reference from both Christ and the Apostle Paul is that Christ does not have a beginning. This is why, during his trial, before they decided to crucify him, when they said basically, are you God? He said, I am. This is claiming the name of the Old Testament that was revealed to Moses on Mount Sinai. So who was it that walked with Adam and Eve in the garden? Many times the speculation from the holy fathers is that it was the pre-incarnate Logos, Christ, that he actually was with them in the garden, that he interacted in various ways in the Old Testament.