Hold up
We saw in linlin’s backstory that John Giant had already joined the marines.
So there were giant marines at this time, the WG was just super selective over which giant they recruited.
John was an orphan. The other giant marine we somewhat know the origins of is Saul, who we specifically know is not from Elbaf.
My guess is the WG was trying to ensure that giant marines weren’t going to be Nika sympathizers. Hence avoided elbaf giants, who knew of Nika.