The British No 1, seeded 11, has become a master of winning these early Grand Slam matches and so it proved once again, a run of 10 straight games helping him to a 7-6, (7-3), 6-0, 6-3 victory over a player ranked 143.
Norrie only arrived in Melbourne late on Saturday night after a heartbreaking loss to Richard Gasquet in the final of the ASB Classic in his home city of Auckland.
That gave him only one day to prepare for this match but he carried a lot of confidence from a run of six victories to start the season, including over Rafael Nadal at the mixed-gender United Cup, as well as his exploits of the last two campaigns.
"I was pretty nervous but I managed to relax in the second set there and close out a tough game. Not my best level but I'll build on it," Norrie, who reached the semi-final at Wimbledon last year, said.
"I enjoyed the match after that tricky first set."
A good run here could see Norrie return to the top 10 and he was his customary relentless self as he wore down 18-year-old Van Assche.
The Frenchman, who won the junior title at Roland Garros in 2021, is considered a big talent for the future and twice recovered from a break down in the opening set.
Norrie became a little wayward off his forehand but tightened things up in the tie-break and from there kept constant pressure on Van Assche, who will have learned a lot from the encounter but was not quite up to the task here.
The 27-year-old has set his sights high for the next few years as he aims to become No 1 in the world.
"I want to be world No 1, that's a big goal for me. Obviously, there's a lot of things I need to tick off first, I have not been top five yet so it's a goal I want to put in my mind to make sure every day I am practising towards that and trying to be the best player in the world," he said.
"It's a tough goal and a long way to go."
He will face either Thiago Monteiro from Brazil or Frenchman Constant Lestienne in the second round. The other danger player in the quarter is sixth seed Felix Auger-Aliassime.