Michael O'Neill's men get their campaign up and running against Hungary in Budapest and Brunt is confident they can end a rather barren run after being drawn into Group F with Faroe Islands, Greece, Romania, Finland and Sunday's opponents.
Since reaching the 1986 World Cup in Mexico, where they were knocked out in the group stage, Northern Ireland have failed to reach a major tournament.
Under the stewardship of Lawrie Sanchez and then Nigel Worthington, they finished third behind Spain and Sweden in the qualifying campaign for Euro 2008, despite beating Luis Aragones' side.
In fact, Northern Ireland have never reached the European Championship finals, but Brunt feels this is their best chance yet to end that.
The 2016 edition will see 24 teams take place rather than just 16, as was the case in its old format, and Brunt, one of only four Premier League players in the squad, is hoping to take advantage.
"It's going to be tough," he told Sky Sports. "But with the extra teams going through this time it's got to be the best chance we've had for a long time.
"We've got to be confident. It's important we get off to a good start, but the other teams will be thinking of that as well, especially Greece, given that they were in the World Cup.
"You don't get to the World Cup knockout stages without being a good side, so everyone expects them to qualify but there's second and a play-off place up for grabs.
"This campaign is going to be big for everyone. We want to score more goals because if you take away David Healy then you could probably say it's a problem for most of us in the camp.
"But if getting a result means more defending I'll take it. It really doesn't matter who scores – even if our goalkeeper Roy Carroll smacks one in."
Despite Brunt's comments regarding confidence, Northern Ireland approach the match in dreadful form, having won only one of their past 22 matches.
Hungary's own form will by no means scare the Irish, but a 2-1 friendly loss to Finland in March is their only defeat from their last five games.
The two countries have only played each other two times since the turn of the century, with Hungary winning on both occasions.
Vladimir Koman, Leandro and Tamas Kadar missed each of the last three Hungary internationals and look set to be unavailable once again.
However, coach Attila Pinter has been able to call upon the services of captain and key player Balazs Dzsudzsak after he sat out of the friendly win over Kazakhstan in June.
O'Neill has been given a few selection issues of his own in the build-up, with Ben Reeves (hamstring), Stuart Dallas (leg) and Ryan McLaughlin (knee) all pulling out with injuries, while Alex Bruce has been excused as his wife prepares to give birth.
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