The 22-year-old saw teammates at the Giants' Olympic Park base on Friday for the first time since his operation.
"His surgery went really well and he's in really good spirits," GWS veteran Callan Ward said.
"I think he'll spend a couple of weeks away from the football club but he has a big smile on his face and it's great to see him here today."
Hill has to avoid sweating for two weeks because of the wound from the operation but will slowly build up his fitness program from there.
He will start with cross-training before resuming running and weights sessions next month.
That plan leaves the door open for a playing return at some stage this season but Hill's health remains the priority as Giants players and staff rally around him.
"In terms of a return to play, at the moment I don't think it really matters for him," Ward said.
"He's trying to get everything else right and when that will be, it will be."
Hill has played in all 11 of the Giants' games so far this season, including the most recent outing against Brisbane, which came after his cancer diagnosis.
The livewire forward requested a trade to Essendon at the end of last year to be closer to family in friends in Melbourne, but was denied a move.
GWS held him to his contract, which runs until the end of this season.
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