Dr Helmut Marko expressed relief as practice sessions got underway in Melbourne.
While early title favourite Lando Norris set the initial pace, signs of a fiercely competitive 2025 season also emerged.
"The results are really close," Red Bull adviser Marko told ORF. "Thank God we are not that far away.
"The four strongest teams - McLaren, Ferrari, Mercedes and us - are very close, and the four tenths that Max (Verstappen) lost is not representative.
"It will be an exciting event and it is all about fine-tuning."
Marko's remarks come after McLaren's top driver Norris downplayed his position as the clear championship frontrunner this year.
Mercedes' George Russell had earlier stated: "Let's not kid ourselves - we know that McLaren are without a doubt the clear favourites right now.
"They looked absolutely dominant in testing and I'm sure they are the ones we have to beat."
Many highlight Norris' standout long-run pace from the recent Bahrain test. Norris, however, countered: "Oscar (Piastri) did a run the next day that was much slower.
"Not because he drove worse, but simply because the conditions on the last day were considerably slower. So I'm quite surprised that so many people are being so short-sighted - especially people you wouldn't expect.
"I suppose everyone wants to play the dark horse. I know how much fuel and other things Ferrari used in many of the tests. I think people will be surprised how fast they'll be this weekend," Norris added.
Sure enough, Charles Leclerc led the second session, ahead of the McLarens. Verstappen's gap to the top, meanwhile, grew to six tenths.
Alpine adviser Flavio Briatore believes Red Bull and Verstappen's era of outright dominance is "over".
Yet he told Corriere della Sera newspaper: "It was incredible how Max won last year even when the car wasn't competitive. He's capable of magic - works of art. He can do anything."
Marko, meanwhile, cautioned that Red Bull had improved the car since the Bahrain test ended.
"There was concern when we realised we weren't at McLaren's level," he told Krone newspaper. "And when the new parts that arrived on the last day only partially worked.
"But afterwards, Max was on the simulator a lot and gained some valuable insights."
Mercedes boss Toto Wolff, speaking to Sky Deutschland after Friday's sessions, said: "My first estimate is that Norris and (Oscar) Piastri will be ahead on one lap."
