It probably means before the author was born, he had been there. But we need more context.

"Before my time" is an expression meaning before I was born or remember or was around. An example is I was born in the 1980s, so I could say a song from the 1950s was "before my time." He was there way before my time is likely referring to someone working somewhere or being somewhere a while before the author was there or possibly even born. But I would need more context to say specifically.