The Woking-based outfit lie just 42 points behind Red Bull in the constructors' standings, and have closed the gap in recent races.
Both Lando Norris and Oscar Piastri have secured their maiden wins this calendar year, and Brown is backing the entire team to achieve even bigger things.
McLaren now lie closer to seasonal silverware than they have in over a decade.
Their last title came in the drivers' championship with Lewis Hamilton in 2008, when the then-young Brit secured his first of seven titles in his sophomore season in the sport.
Before that, McLaren won consecutive titles with Mika Hakkinen in 1998 and 1999, including the double in the former year.
Their golden era came in the 1980s with legendary drivers Niki Lauda, Alain Prost, and Ayrton Senna.
Silverware has been hard to come by in recent years, with just three race wins since 2012.
However, Brown is backing his papaya army to return to the glory of those historic days.
"It's all coming together," he told Motorsport at the Belgian Grand Prix.
"We've got our great investment from our shareholders and our sponsors. We've got great drivers, we've got a great technical team, and the entire leadership team, the technical team need the resources, the fan base, the corporate partner base in order to be able to do what they're doing."
McLaren's recent upturn in form cannot be disputed, with all areas of the operation seeming to be working in harmony. Brown went a step further, though, claiming every department had 'world championship material'.
"Andrea [Stella, McLaren team principal] uses the term 'world championship material' and I'd like to think all departments, which feed into performance, either directly or indirectly, are all world championship material," he said.
With ten races to go in the 2024 season, McLaren are on cusp of realising that world championship potential. If they can catch Red Bull and get over the line, Brown's claim will be vindicated.