The sides meet at the Municipal Stadium in Poznan in the opening round of Group C games with both knowing three points on the night could prove crucial to their hopes of making the quarter-finals with Spain and Italy waiting in the wings.
Ireland's recent form against manager Giovanni Trapattoni's home country has been more than impressive, but a positive start would send them into their second game against reigning world and European champions Spain knowing they could be genuine candidates to emerge from the group.
Keane said: "It's vitally important. Of course in any competition, you want to start off straight away as well as you can and try to get points on the board because we know that in the group, anybody can beat anybody.
"We just have to take each game as it comes, as we always say. We will focus on Sunday's game and see what happens after that.
"Hopefully we will be talking after that game with three points in the bag."
Keane, of course, is Ireland's record international goalscorer with 53, and a significant addition to that tally over the next week or so could prove key to their hopes of reaching the last eight.
However, he could yet find himself playing in a more withdrawn role with Trapattoni having once again seen his midfield at times overrun during Monday night's 0-0 friendly draw in Hungary.
A similar thing happened during the 3-2 qualifier defeat by Russia at the Aviva Stadium when the Republic failed to get to grips with a team fielding a lone striker and a man probing from deep, and the 73-year-old has spoken on more than one occasion - indeed, has also implemented the plan in a couple of games - of Keane occupying the "number 10" role perfected by Italy's Francesco Totti.
If that proves to be the case in Poland, Keane insists he will be happy to do as he is asked.
The 31-year-old LA Galaxy frontman said: "It's something I have done. I have kind of played two different roles, if you like, at club level and international level.
"At international level, the pressure is on me to score the goals, but at club level, I kind of play as that number 10 anyway.
"Maybe if the manager wants me to do that role, which I am sure in certain games, he will probably want that, it's something I have done before, so it wouldn't be a problem.
"We have played the same system since the manager took over, so the players are certainly used to that.
"But if there was an adjustment, it would be little minor things, I think.
"As players, you are always set different roles when you go out on to the pitch - myself, for example, to just sit on the holding midfielder and don't let him dictate the game too much.
"It would be little, small things like that, I wouldn't say it would be formation changes. We wouldn't automatically just go to 4-3-3 when we haven't done it for a long time."
The players enjoyed a spa day yesterday after being given a break from training, but were back in harness this morning as they started to prepare for Sunday night.
They did against the backdrop of a piece in the FT.com's Alphaville blog which suggested their squad has the lowest aggregate value at the finals, which clearly amused Keane.
He said with a smile: "They said that, did they? The cheapest squad? I wouldn't disagree with that, then."
Whatever disadvantages Ireland may or may not have, they embark on the tournament with high hopes of making an impression, and with Greece's 2004 triumph in Portugal providing the perfect inspiration.
Asked if his team could do something similar, Keane said: "I hope so, I certainly hope that's the case.
"Listen, we are not coming to this competition to make the numbers up. We are here to do as well as we can for the country and hopefully go as far as we can.
"We go into every game in every competition believing that we can win it."
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