Nobody seems to know how brilliant chess moves come about. But there is a myth about them usually repeated by people who play chess, but more at a casual or even sparse amount.
This myth is that the "brilliant" chess move came from an hour or so of deep analysis by a grandmaster, who suddenly screams mentally "EUREKA!!". And he wins the game, the brilliancy prize and the praise of his peers.
Reality is much different. I have played a few brilliant moves in my day. I only found one that won a game I thought was even. One where I found a deep 6-move swindle to win a completely lost game. And a couple of times I found forced repetition draws to save myself from losses. But these took me a lot of time on the clock, as the myth would suggest. But I am not a grandmaster.
It is White's move, GM Averbakh vs Kotov, Candidates Tournament, 1953.
White is in time trouble and played 30. Ne2. Kotov as Black replied almost instantly 30. ...Qxh3+!!.
This is remarkable because in Kotov's book Think Like a Grandmaster, Kotov declares that a grandmaster is obligated to analyze every reasonable candidate move in considerable detail.
Kotov was not in time trouble and had 40 minutes to make the 40 move time control, but played the first candidate move that popped into his head.
That is what he said he did. But possibly he had found and analyzed that move during his opponent's longer thinks. Who knows for sure.