The 17-year-old crossed the line in 19.84 seconds, a time that eclipsed his own national record by 0.2 seconds but which will not count as a new mark due to a wind speed of +2.2 metres per second.
"Feels pretty good," Gout said. "That's what I've been chasing, I've been chasing getting that sub 10, focusing on my first hundred and that's exactly what I did.
"I got out, I sent it. Top speed is my gift. I used it, took off and I got sub 20 so I couldn't be happier.
"I think (I'm) maybe one of the youngest to ever win a men's national title, so it definitely feels great. Couldn't be happier for sure."
Gout's pre-race rival Lachlan Kennedy was disqualified for a false start and, as a result, the youngster hesitated out of the blocks before powering down the straight to leave the competition battling for second.
Peter Bol set a national record of 01:43.79 seconds to win the men's 800m as he continues his return to form ahead of the World Athletic Championships in Japan in September.
"I should have been at this level a few years ago; obviously, I had some interruptions," said Bol. "But to be back here, to know this is where I belong is great. I always knew I could do it, it was just a matter of time."
Bol finished fourth at the Tokyo Olympics in 2021 but his career was disrupted after he was provisionally suspended in January 2023 for returning a positive test for synthetic erythropoietin in out-of-competition testing.
The provisional suspension was lifted a month later and the investigation was dropped in August that year, clearing Bol to run at the 2023 World Athletic Championships, where he was eliminated in the heats.