Near the end of the first quarter on Monday, Julius Randle, the Knicks’ burly All-Star forward, pulled up and banked in a shot from 25 feet. It was the kind of shot that might have sent him to the bench in a previous era of basketball, or even on a previous Tom Thibodeau-coached team. On Monday, it was Randle’s fourth 3-pointer in 12 minutes.

It was also a shot emblematic of the new-look Knicks: This year’s version is taking 3-pointers. Lots of them. In the first quarter alone against the Toronto Raptors on Monday, 13 of the Knicks’ 19 shots — and five of Randle’s — were from behind the 3-point line. The approach has been a hallmark of the new Bing Bong-era of the Knicks, and it is part of the reason Thibodeau’s team is off to a 5-2 start, the franchise’s best since the 2012-13 season.

In their second game, the Knicks set a team record for most 3-pointers in a game with 24, en route to a 121-96 victory. This year, the Knicks are taking 40.6 deep shots per game; that is good for eighth in the league and is 10 more per game than last season, when the Knicks ranked near the bottom of the league in attempts.

“With the 3, you can make up ground quickly,” Thibodeau said. Or not. On Monday, the Knicks tried 36 of them, made less than half and absorbed their second defeat of the season, a 114-103 loss to the Raptors.

While the Knicks didn’t try as many 3s last season, they were accurate in the few they shot: 39.2 percent over all, good for third in the N.B.A. This year, they are near the top in accuracy again, only with more volume. At their current rate, the Knicks are on track to have a top-five offense for the first time since that 2012-13 team.

The Knicks have also picked up their pace, if only slightly. Last season, the Knicks were dead last in fast break points. This year, they are 22nd.

“I think this is the fastest I’ve seen them play for a long time,” Toronto Coach Nick Nurse said before Monday’s game.

The early positive returns on the Knicks season are the clearest indication that Thibodeau — a coach known for stubborn adherence to his brand of physical basketball — is capable of adjusting to the new realities of the modern N.B.A. He has reinvented the team’s offensive identity with a simple mantra.

“Drive the ball, get your spacing, make your rim read — keep the game simple,” Thibodeau told reporters on Monday, adding, “When we do that, we’re really good.”

Still, the transition to a more 3-pointer-heavy offense wasn’t simply a case of telling the team to shoot more of them.

Thibodeau received a significant assist — or by some interpretations, had his hand forced — by a shift in personnel. Last season, the Knicks’ starting point guard was Elfrid Payton, a nonshooter whom opposing defenses would often ignore on the perimeter, clogging the paint for Randle and leaving him more susceptible to double teams. This year, Kemba Walker has occupied that spot, and he entered Monday night shooting an almost assuredly unsustainable 57.9 percent on 3-pointers.

It is not just having better shooters. Walker and Evan Fournier are superior ballhandlers, and their arrival, along with the improved RJ Barrett, allows the Knicks to more easily break down defenses and create open opportunities on the outside.

Having a healthy Mitchell Robinson in the starting lineup has been a boost as well. At 7 feet, Robinson draws attention at the rim as one of the Knicks’ best alley-oop threats at the basket. That gives the Knicks more space on the perimeter to create open looks.

If there is a worrisome sign, it is on the defensive end, where the Knicks have been below average — something highly unusual for a Thibodeau-coached team. While the Knicks have been taking a lot of 3s, they also give up a lot — more than all but two teams in the N.B.A.

Their new acquisitions — Walker and Fournier — aren’t known for their defense. On Tuesday, the Knicks surrendered looks — and points — on the inside and outside to Raptors forward OG Anunoby, who scored 36 points. While Toronto made only 14 of its 42 3-point shots, it was enough to pad a double-digit lead in the second half.

Seven games isn’t a huge sample size. Inevitably, some shooting numbers, like Walker’s, will return to earth. But the new-look Knicks, with a sleek, contemporary offense, seem to have the personnel to merit their early optimism.