The 25-year-old striker is one of four forwards in Trapattoni's 23-man-squad vying to partner Robbie Keane in their opening group match against Croatia in Poznan
The West Bromwich Albion forward is desperate to line up against Croatia in Ireland's opening Group C encounter against Croatia. With all-time record goalscorer Robbie Keane seemingly assured of his place in Trapattoni's first XI, Cox faces a battle against Kevin Doyle, Jonathan Walters and club team-mate Shane Long to support the LA Galaxy striker.
Having scored in the 5-0 win against a Tuscan Select XI last time out, Cox his hoping he can stake his claim further against Hungary on Monday.
He told RTE Sport: "I just want to get some game-time, that's it. I want to show what I can do.
"Hopefully by doing what I did the other day. Scoring goals and putting in decent performances, that's how I show what I can do."
Competition for places is hotting up as the tournament draws closer, and Cox revealed there is a marked increase in the intensity of training as a result.
Cox said: "We can't wait to get started. This is what we all want to do and these are the competitions you want to play in.
"We have a good tight unit, so I don't see why we can't prove a lot of people wrong who are doubting us at the minute.
"All 23 are fit and healthy, which gives the manager headaches for selection come the games we have in front of us."