Although Brown admits Red Bull, who have won all 12 races to take place to this point, and Max Verstappen remain out of reach, the American underlines McLaren can target being second best by the end of 2023.
“Red Bull are an incredible team,” Brown told Austrian outlet Laola1.
“We try to get close to Max [Verstappen], but every time you think you’re close he pulls away. It’s impressive to watch him.
“To be the second fastest team at the end of the season, best of the rest, would be very satisfying. There’s still a long way to go, but we’re definitely back in the game.”
McLaren’s torrid opening to the year was attributed to missing development targets on the launch-spec version of its MCL60 car.
That prompted a reshuffling of its technical department, with Technical Director James Key being ousted in favour of a newly-formed three-pronged arrangement.
Brown has credited the entire team for the drastic turnaround it has enjoyed.
“There’s a lot of things playing together excellently,” he explained.
“Our aerodynamics upgrades have been impressive. I take my hat off to that.
“The drivers are now showing their potential. They also did a very good job before, but now they can be even more convincing in the improved car.
“The first laps at Silverstone were a highlight, my pulse went up again rapidly. It’s a shame that Oscar [Piastri] was denied a podium.”
Only Red Bull has outscored McLaren in the five rounds to occur since the British entry unveiled a raft of substantial upgrades.
McLaren has eclipsed Alpine to reside in a comfortable fifth in the Constructors’ Championship at the summer break.
However, it still remains 88 points shy of Ferrari in fourth, with the Italian marque only five adrift of Aston Martin one position above.
Mercedes, meanwhile, uphold a healthy 51-point advantage in second place – but the German manufacturer is a colossal 256 points behind Red Bull, with Verstappen’s points tally alone enough to retain the World Champions advantage at the top.