Tom Brady jersey that the quarterback wrote "G.O.A.T" on has just hit the auction block -- and TMZ Sports has learned it's so rare, it could fetch over $600,000. Check out the uniform ... it's an all-black Buccaneers kit that Brady wore when he carved up the Atlanta Falcons on Jan. 3, 2021, just a few weeks before he won Super Bowl LV in Tampa. Goldin -- which is handling the auction -- tell us it's believed to be the only game-worn jersey in Brady history that he's written "G.O.A.T." on. We're told it's such a one-of-a-kind piece, getting over half a million dollars for it should be no problem. Bidding ends next month ... hope you're saving up that Christmas cash.