But in a football sense, the two were strangers, and Kelce wasn't alone among his Kansas City Chiefs teammates.
"I'm pretty sure three or four of the guys out there on the field had never caught a ball by Matt, even in practice," Kelce said. "I know I hadn't. It was just going out there and playing within the rules of the offense and trusting the guy to be able to put the ball somewhere."
The Chiefs played something more than backyard football after the veteran Moore replaced the injured Patrick Mahomes in the second quarter of their 30-6 win over the Broncos. Moore completed 10 of 19 passes for 117 yards, including a 57-yard touchdown pass to Tyreek Hill during which the two looked well-acquainted.
Hill may have been the only Chiefs receiver to be familiar with Moore, their bond coming on the scout team at practice recently as Hill was preparing to return from his injury.
"I had a chance to go against the defense and he was the quarterback," Hill said. "We [were] out there drawing up plays. I was [Houston's] Will Fuller, he was Deshaun Watson. Me and him, we kind of got a connection going."
But to Kelce's point, the offense was largely basic once Moore replaced Mahomes. That was partly by choice -- the Chiefs moved to a 20-6 lead shortly after Moore entered the game -- and partly by necessity.
That's why things should be more refined for Moore if he has to be the Chiefs' starter for an extended period of time. Sources have told ESPN's Adam Schefter that Mahomes could return in three weeks, if not sooner. The Chiefs have 10 days between Thursday's game against the Broncos and Sunday's game against the Green Bay Packers (8:20 p.m. ET, NBC) and Moore will have the benefit of some practice time with the starters. The Chiefs could design their game plan around his abilities rather than those of Mahomes.
Moore didn't even have the benefit of a training camp or a preseason with the Chiefs. He arrived in late August after the Chiefs lost their other veteran backup quarterback, Chad Henne, to a broken ankle. Moore was out of football last season, and hadn't played in a game since 2017.
"He's got ice water in the veins," coach Andy Reid said when asked what he learned about Moore against the Broncos. "He doesn't flinch. There's no panic. He says, 'I'm good. Just call [the play] and let's roll.'
"We need to just get a little of that rust [off]. We're good whatever direction this thing goes."
The 35-year-old Moore was preparing for life after a playing career earlier this year. He worked for a time in the Miami Dolphins' scouting department and was helping to coach his former high school football team in California when the Chiefs called.
Moore had 10 NFL seasons before joining the Chiefs with 49 games, 30 starts and a 15-15 record for the Dolphins and Carolina Panthers. His previous game happened on Nov. 26, 2017 when he threw for 215 yards, one touchdown and two interceptions for the Dolphins in a 35-17 loss to the New England Patriots.
"I've played in this league before," he said. "Just like everybody I've had my ups and downs. ... It's been a wild half a year or whatever. You've just got to move forward and go."
He put his experience to use and figured some things out on Thursday night. He knew of Hill's speed -- he told himself not to leave the throw short on the touchdown pass -- and made a nice throw by lofting the ball over a defender who was in the passing lane.
But like many of his teammates he was largely guessing.
"There were a couple of times when he was working back in," Moore said of his practice connections with Hill. "There were a couple throws in practice. Not many."
Moore had the luxury of playing with a comfortable lead for much of the game. The Chiefs were inside the Denver 5 when he entered the game. He ran three plays and the Chiefs kicked a field goal.
The defense scored on the next Denver possession by recovering a fumble for a touchdown.
He figures to be under more pressure against the Packers, but at least Moore has some momentum.
"Matty came in full of energy and ready to rock and roll," Kelce said. "Matty Moore [is] 1-0."