This comparison is totally absurd.
Tom Brady never represented his country vs. the world when his country did not consider him a full citizen and won Olympic Gold for his country. Tom Brady never went one on one and defeated the scariest puncher in boxing becoming the youngest heavyweight boxing champion. Tom Brady never stood on moral and religious principles of right to call an unjust war unjust. Tom Brady (who actually cheated) never had his title, livelihood, and status stripped because he stood against unjust power. Tom Brady did not have the prime of his athletic career taken away unjustly as a conscientious objector to war. Tom Brady never had to overcome losing what was call the "fight of the century" and still have the fortitude to continue to win and lose, win and lose, and win and lose proving he was what he said..."The Greatest of All Time".
Tom Brady never took the time out of his schedule to talked a man from off the ledge of a building keeping him from committing suicide. Tom Brady never showed the resolution to change when he was wrong to change to what was right and then promote that change. Tom Brady never went to a dictator and negotiated the release of American hostages. Tom Brady has not been world recognized as the Greatest of All time as an athlete, leader, humanitarian, symbol for peace, truth, and righteousness in every country of the world.
Therefore, I see absolutely no comparison between Tom Brady and Muhammad Ali. Therefore, there is no need for a discussion of who and for whom the term G.O.A.T was originated and used.