The Dons have beaten St Johnstone and Morton, in the Scottish Communities League Cup, in the past seven days.
And Brown believes Sunday will be a good challenge for his players against Hearts.
When asked whether Aberdeen could challenge, Brown responded: "Well, I'm not saying that. I'm saying we'll do the best we can and try to improve on last season.
"Other people think we've started in a positive manner and we're likely to challenge, I'm not saying that.
"This will be a good yardstick against Hearts and I expect Hearts, Dundee United and Motherwell to be the teams chasing Celtic. I'm very hopeful that Aberdeen will join that group."
Brown watched on as John McGlynn's men lost 1-0 against Liverpool on Thursday night in the Europa League.
Defender Andy Webster scored a second-half own goal but deserved better and the former Scotland boss was encouraged by the Tynecastle side's display.
He said: "I was very impressed with the Hearts performance. Certainly, they didn't deserve to lose that match against Liverpool.
"But unfortunately, the own goal was horrendous.
"Hearts played well and they proved they will be difficult opponents.
"They are a force in Scottish football and they have been for some time, where as, we haven't and they are the cup holders, so we've got a major assignment on Sunday."