Gawn was colossal in the ruck as Kysaiah Pickett starred and Jake Melksham kicked four goals on return in the 16.13 (109) to 14.5 (89) win at the MCG on Sunday.
It gave the Demons an impressive 3-1 start to life under King ahead of a meeting with lowly Essendon in Gather Round.
"You're never sure how quickly it can click and to get it to this point so far is pretty encouraging," King said.
"I've got an amazing coaching group that believe in their players and I think the players now are starting to believe in themselves."
Pickett dazzled with 25 disposals, six clearances and one goal against a star-studded Suns engine room and Melksham, in his first game of the season, led the way in attack.
The veteran forward also produced the highlight of the day with a spectacular mark on Sam Collins' shoulders before converting his long-range set shot.
Gawn (22 touches, one goal) and experienced recruit Jack Steele (26 disposals, 11 clearances) were key contributors, and Latrelle Pickett added spark in attack with one goal and eight score involvements.
"I want them (supporters) to get excited about what they're seeing," King said.
"(We've got) a team of experienced legends of our club that have won the ultimate and a group of young men that are experiencing things for the first time.
"We want to be a team that can challenge in every phase of the game and be dangerous with and without the ball and be fun to watch."
Gold Coast's first defeat of the season came in the absence of former Demon Christian Petracca, who missed what would have been his first clash with his former side due to a hamstring injury.
Fellow midfield star Matt Rowell (13 disposals) got through his first game of the season after overcoming a finger injury and captain Noah Anderson (22 touches, seven clearances) fought hard.
Ben King (three goals), Ethan Read (three), Jed Walter (two) and Zeke Uwland (two) all kicked multiple goals, but the Suns were thoroughly outplayed by an exuberant Melbourne outfit.
The Demons dominated contested possession (+22) and clearances (+11), leading to a one-sided inside-50 count (59-45).
"The middle part of the ground we got absolutely spanked," Suns coach Damien Hardwick said.
"Max Gawn was by far the best player on the ground and we've been very fortunate with Jarrod Witts.
"We've probably got the second-best ruckman in the competition but he got well and truly beaten today.
"He'll bounce back, there's no question about that, but I thought our midfield had their colours lowered as well."
