Even if a coach inherits a mess, Year 3 is supposed to be the time when the mess yields to the new man’s method. He has had — or should have had — time to rustle up enough players capable of playing basketball the way he wants it played. If Year 3 isn’t exactly a make-or-break time, it’s definitely a show-and-tell season.

This is Year 3 for Brian Gregory, imported from Dayton over bigger names — some of whom had little interest in the job — to lift Georgia Tech back to prominence. Year 1 was the inevitable wipeout: The Yellow Jackets lost 20 games and failed to break 40 in three of them. Year 2 was better (16-15) but nothing special, although a late-season road victory over ACC champ-to-be Miami affixed a smiley face.

A more robust Tech roster figured to make real strides in Year 3, and that could well happen. Early returns, however, had been uninspiring at best and deflating at worst. After the accustomed victory over Georgia — which as of Tuesday ranked 342nd among 351 Division I teams, according to ESPN’s Daily RPI — nothing good had happened for the presumably bigger and better Jackets.

They lost 82-72 at home to Dayton, and it looks kind of bad when the guy you hired can’t beat the team he used to coach. They trailed at halftime against North Carolina A&T. They went to Brooklyn and lost to Ole Miss and St. John’s by an aggregate 21 points. That dropped Tech to 5-3; by way of contrast, last year’s middling team didn’t lose its third game until Jan. 5.

When you lose three by the first week of December, math begins to work against you. If a team goes 9-9 in ACC play — and Tech hasn’t gone even .500 in the league since 2006-07 — that would make 12 losses. Another in the ACC tournament would make 13. Thirteen losses would be close to the max for any team that aspires to an NCAA invitation. Which is why Tuesday night’s game against Illinois in the ESPN-hyped ACC-Big Ten Challenge was something of a big deal, even if it was only Dec. 3.

The Illini entered unbeaten but unranked, their best victory coming over UNLV. Illinois went 23-13 last season and made the NCAA tournament, even winning a game once there, but that team lost three starters and is recalibrating. Tech, by way of contrast, had replaced point guard Mfon Udofia with Trae Golden, a senior-to-be who left Tennessee in May and was granted a waiver to play immediately by the NCAA.

His name alone made Golden a great Tech addition, but for a team with good big men (Daniel Miller, Robert Carter Jr. and Kammeon Holsey), a gifted wing (Marcus Georges-Hunt) and a perimeter shooter (Chris Bolden), the arrival of an accomplished guard figured to put the Jackets within sight of the NCAA bubble. As advertised, Golden has been good. Until the late going Tuesday, his new team had been less so.

The Jackets trailed by nine points midway through Tuesday’s first half, but surged to a 36-33 lead on the strength of offensive rebounding and the deftness of Carter, a power forward who can shoot like a wing. Tech built its advantage to 44-39 on Carter’s baseline hook early in the second period, and there the Jackets stopped.

The Illini, who had been content earlier to hoist 3-point shots, started beating Tech to the hoop. Illinois also changed its defense, junking its zone to pressure the ball, and the Jackets responded as if they never had been guarded. Every possession became a 30-second journey to a forced shot, and inside the final seven minutes the visitors led 60-48.

Whereupon the inspired Illini began trying, perhaps without meaning to try, to milk the clock. Illinois went scoreless on seven consecutive possessions, and the Jackets were suddenly emboldened. This was the Tech team we’d been waiting to see, big and strong and capable of making tough shots.

Sub Solomon Poole hit a trey from the corner. Georges-Hunt made two free throws and then a scored on a baseline drive to tie the score at 60. Illinois retook the lead. Tech overrode it again. Carter sank a 3-pointer with a minute left to draw the Jackets within a point, and Miller slipped underneath to put them ahead with 24 seconds remaining.

“When I think of how I want Georgia Tech to play, that’s how I envision it — playing with toughness,” Gregory said. Then this: “We’ve got a ways to go, but if you give that kind of effort, you’ve got a shot.”

It’s far too soon to make too much of one game, but any team anywhere can use a rousing victory any old time. Tech’s rousing victory seemed exquisitely timed.