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Givens' side face Belgium at Galway's Terryland Park knowing a win will see them through to the play-offs in early October.
That would leave Ireland just two matches away from playing in the finals for the first time in their history.
Although Belgium are top seeds and group favourites, Ireland go into the game on the back of a seven-match unbeaten run, including six successive wins.
After seeing so much promise fall by the wayside over the years, Givens is relishing the occasion as he said: 'We've given ourselves a chance to do something.
'This match will be tougher because Belgium are a better side than Greece, but we have to do this.
'Ideally we will win the game, top the group and then we can't be caught. What we can't do is lose.
'In many respects it is a must-win game, and as such the biggest I have been involved in with the under-21s.
'I've always said since I took on the job that the most important part of it was about development, seeing players promoted to the seniors.
'But it would also be fantastic if we could compete in the finals of the European Championships.
'That has not happened to us so far. We've struggled for various reasons.
'So for once, and for someone who doesn't like to lose at anything - not even a game of cards with the kids - it's about time we had some success.'
Givens refuses to take the credit for the Republic's resurgence in fortunes as the current hot streak follows a nine-match winless run.
'I don't think there has been any kind of turnaround other than we now have a solid group,' added Givens.
'They've performed well, have won matches and that has resulted in a rise in confidence, with the win over Greece the best in my time in charge.
'I've coached groups of players who have had chances to progress before, but it has not happened.
'Now this lot have their own chance simply because they've worked hard for it, and I hope they are able to take it.'
Givens was forced to make two changes to his squad earlier this week, with Garry Dicker and Anthony Stokes replacing Darron Gibson and Jay Tabb due to knee and hernia injuries respectively.