I think your right. And if I remember, the famous photo was taken after the Marines had already raised the flag. The photographer saw what they did - liked it - and had them do it again so’s he could take a picture.
I guess I could wiki this and see.
no, he did not stage it
they raised the second flag because the first one was too small
and Rosenthal and Genaust were there for the second one
Genaust was the first photographer of the first flag and the men who put it up