You mean, how do we know that's what Apostle John was talking about in that verse, that Satan was the first sinner? It's pretty easy to figure out, because in Ezekiel 28 God shows that He originally created Satan perfect without sin. And we surely know Satan was without sin at what time? and that was when he was in Eden at God's Altar without sin like the Ezekiel 28 Scripture shows.
We well know that was not in the time of Adam and Eve in God's Eden, because Satan was there as tempter by that time, showing he had already fallen. We have to go back in time, before Adam and Eve in God's Garden.
The parable in Ezekiel 31 analogous to Satan is another clue when Satan was originally perfect in following God, but that chapter is kind of difficult if one hasn't studied many of the symbols given there in other OT Books. It goes deeper than the Ezekiel 28 example does.