Wales are also struggling to fill the tight-head prop role left by Tomas Francis, who has been missing since the 2023 World Cup following his move to French club Provence.
Gatland insists Francis has not retired from international rugby but the Wales coach is looking for a long-term successor.
Henry Thomas, Leon Brown and Keiron Assiratti were ruled out of the summer trip through injury, while Dillon Lewis is not fit for the first Test.
That paves the way for Bath prop Griffin, who was born in Sydney but qualifies for Wales through his parents.
“It’s one position we’re probably the most exposed at,” said Gatland.
“We just haven’t had a consistent tighthead who is playing week-in, week-out. The last one was probably Tomas Francis, but we need to get someone on the field and develop some experience.
“Archie is explosive and technically excellent. Unfortunately in the Six Nations he picked up an injury right at the start. It’s good to see him back and we would just like to see him play some more rugby.”
Griffin will come up against Australia’s most-capped player, James Slipper, who will be playing his 135th international.
“That’s how you learn your trade – it’s a hard one,” said Gatland.
“I don’t expect any front-rows or tight forwards to be any good until they’re 27, 28 or 29. I know James Slipper is a little older than that and his record speaks for itself.
“With [Taniela] Tupou on the tighthead, they’ve probably thought that’s one area they can get an advantage and dominate.”
Wales aim to solve the scrum problems they had against South Africa last month.
“It’s definitely been a focus in terms of tightening it up this week,” said Gatland.
“We can’t operate a game with our scrum being under that sort of pressure.
“I don’t think Archie will be fazed, but it’ll be a learning curve for him. As an ex-front-rower myself, things don’t always go as you expect.”
