the trick is to keep breathing

I'm not entirely sure that Squall ever figures it out. He's not the most clueful boy in the world, and he seems frankly derisive of President Laguna right until the end.

Ellone was almost certainly there when he was born (or was that while she was in Esthar?) Regardless, her time traveling shows she knows. She most likely told Matron. The question is, actually, who brought Squall and Ellone to the orphanage, since Raine was dead.

Laguna knows. Kiros and Ward must know, the way they defer to Squall when he pulls Rinoa out of the Sorceress Monument.

Beyond them, I have no reason to think anyone does. I don't think there were enough clues in the Winhull segment of the flashbacks to indicate it.

Although someone might suspect after a while, since Laguna looks a lot like him ETA: whatever Ward may think.

Aurenare raises an interesting point: it is quite likely that Laguna did not know about Squall until later. Surely when Ellone went to the orphanage, he eventually located her and found out. There are clearly some ties between Matron and Laguna, since Laguna left Ellone in her care and/or with the SeeDs.