Sinner, who enjoyed a strong finish to 2023 by reaching the ATP Finals title clash before inspiring Italy to a second Davis Cup triumph, was slightly off the pace after skipping warm-up tournaments in the build-up to the year's first major.
Sinner is targeting another deep run at Melbourne Park after reaching the 2022 quarter-finals but he said his immediate focus was to tidy up his game ahead of his next match against Dutch qualifier Jesper de Jong or Argentine Pedro Cachin.
"It's Sunday today. It's so long to go. But for sure you're aiming for these matches," Sinner said about a potential semi-final encounter with defending champion Novak Djokovic. "But I go day by day. You have one job at a time.
"Today was one player. Wednesday is going to be a different player and you have to try to beat this guy, no? I don't want to say much more about this at the moment, because I feel like there's still a lot of work to do to get to this point.
"Obviously we aim to play big matches in big stadiums, so let's see. It's going to be an interesting tournament."
Sinner grabbed a break in the opening game of the match on Rod Laver Arena and battled to hold in the next before cranking up the pressure with searing winners on both flanks to take the first set.
World number 59 Van de Zandschulp went toe-to-toe with his opponent in the next set before Sinner sealed the decisive break for a 6-5 lead and comfortably doubled his advantage.
Sinner squandered four break points and then surrendered his serve to trail 2-0 as his forehand wobbled slightly in the third set but he responded superbly to close out the match.
Sinner finished the match with 37 unforced errors, many of them coming off his forehand, but he hoped to find his groove as the tournament progressed.
"I feel like best-of-five sets can help me a little bit," he added. "You stay on court a little bit longer. You get to play a little bit longer, which is what I like to do. Then we'll see in the next rounds what's coming."
