"It's still possible, we'll see how all the Canadians are doing in practice and how they're going to prepare for the finals," Parrot told reporters after his score of 97.50 was the best of both heats.
"I'm really happy, it's a beautiful day, it's sunny, good crowd and the course is just perfect.
"There's nothing critical to say about it. The course is awesome from top to bottom and I'm having a blast today," the 19-yar-old told reporters.
Canada's hopes of a clean sweep in the event have been hampered by a injury to Mark McMorris, who still managed to score 89.25 and finish seventh despite a broken rib.
With the top four from each heat qualifying directly for the finals, McMorris will join the rest of the competitors in the semi-final earlier on Saturday.
"Mark broke a rib last week at X-Games, a lot of doctors were on him the whole day from last week, and he actually missed one day of practice because it was hurting too much," Parrot said.
"He's having a hard time, it hurts a lot. I just hope he's going to be fine for the finals and that it's not going to do more damage to his problem."
Unfortunately for McMorris, the standard in the second heat turned out to be much higher than the first, where his score would have been good enough for third place and direct qualification.
That spot was taken by another Canadian, Sebastian Toutant, who registered 87.25.
Charles Reid, the fourth Canadian in the team, came ninth in the first heat with a score of 75.50 and will join McMorris in the semi-final.