The Suns have been steadily building since entering the AFL in 2011 but the maturation of the club's young players this season is noticeable.
Sitting fifth on the ladder with five wins and two losses, McKenna said the club had given itself every chance to make an impact in September.
"We've given ourselves an opportunity. If we stay fit, at 5-2 now that's when I say it's a realistic aim. There's a lot of water to go under the bridge, but (finals) should be (our aim)," McKenna said.
In 2013, the Suns boldly launched their 20.One.3 campaign, with club chairman John Witheriff declaring the team's aim would be to win a premiership in the next three years.
It met with some guffawing but after the Suns' win on on Sunday, the plan certainly looks like having more merit.
"First day of pre-season we looked around, is that (finals) something we wanted to achieve? Course it is," McKenna said.
"The chairman's put a bit of heat on us about winning a flag, but we can give ourselves an opportunity."
Following the Suns' bye next week, the club has two winnable games against the Western Bulldogs and St Kilda to come.
On current form, the Suns could well be sitting pretty at 7-2 and ensconced in the top eight.
McKenna agreed the Suns' win against the Kangaroos was the best in the club's short history, marginally edging out the seven-point win over Collingwood at Metricon Stadium in round 17 last year.
"Yeah, probably in the scheme of the evolution of our football club," McKenna said.
"We understand that finals is a long way off but we wanted to apply the pressure that we would expect to apply to a side in the finals.
"We thought that this was an opportunity against North, who we think are going to be in the finals, so for our boys to go out and do what they did (was pleasing)."
When asked whether the win over North Melbourne was a "coming of age", McKenna was quick to deflect the hype.
"I'm not going to get caught up in saying that some blokes had breakout games and that's it, we're fixed," McKenna said.
"Coming of age is when we can produce that week in week out."
"We're getting close to coming of age, but certainly this year we're getting consistent football and consistent effort."
Twitter: @AFL_BenGuthrie