The Glasgow winger's first cap came as a replacement against France in the 2020 Six Nations but a serious hamstring injury kept him out of action for nearly a year.
Speaking in The Scotsman, Steyn said: "I can't really put it into words. Gregor (Townsend) said before the game that it had been 600 days since we had crowds in and I was like, s*** that means it's 600 days since I last played for Scotland. Just the whole day, the whole atmosphere about it was incredible."
After scoring a 16-minute first-half hat-trick, Steyn finished things off with the final score in the ten-try victory.
Steyn is the first player to score four tries for Scotland since Gavin Hastings did it against Ivory Coast at the 1995 World Cup in South Africa, and the first ever to do it at Murrayfield.
"That's incredibly special," said Steyn. "Scottish rugby is steeped in so much history so to have even a tiny part in that history is pretty humbling.
"I had no idea but, to be honest, you just get those days. Three of those tries were off set-piece plays where I get to dive over in the corner, and then for the other one, Blair (Kinghorn) puts in a cross-kick - he made me work a little bit for it, I couldn't get to it on the full."
Steyn missed out on a second cap at the 2020 Six Nations when the match against Wales in Cardiff was called off due to Covid. Injury then intervened when he tore his hamstring off the bone while training with Glasgow, then suffered a serious setback during the recovery process. He eventually returned for Glasgow at the end of last season and forced his way back into the Scotland squad for the summer tour - only for that to also be postponed due to Covid.
"At one stage I thought someone didn't want me to get a second cap," he said. "I was due to play Wales after France and that got canned the day before. Then we were lining up for the summer, with two opportunities there plus the A game, and we all know the story there.
"At one stage, I was like, someone has it in for all of us, maybe I'll just stay on one and that will be me!"
Townsend praised the winger's tenacity. "He's a great guy to have in the squad," said the coach. "He works very hard, he's very diligent and he's come through some adversity to play for Scotland again."