Although it's not clear why they weren't identified in the films, supplementary material indicates that Green Squadron in fact was present at both the Battle of Scarif and the Battle of Yavin.
The novelization specifically mentions Green Squadron departing Yavin (emphasis mine):
Less than ten minutes later, sirens were announcing the departure of Red, Blue, Green, and Gold Squadrons along with the U-wing transports. Raddus had already contacted all capital ships within range of Yavin or Scarif.
Rogue One: A Star Wars Story Official Novelization Chapter 17
And the film's visual guide names three members of Green Squadron present at the battle:
Broan Danurs, Green Ten:
Attico Wred, Green Four:
Wion Dellems, Green Twelve:
A New Hope
The original 1976 novelization, ghostwritten by Alan Dean Foster, again calls out Green Squadron (emphasis mine):
"Remember," the General went on, "you must achieve a direct hit. Yellow squadron will cover for Red on the first run. Green will cover Blue on the second. Any questions?"
Star Wars Chapter 11
This is reportedly also mentioned in the recently-released short story compilation From a Certain Point of View, but I haven't read that one yet and so can't directly confirm.