The national under-17's women's team play Spain in the semi finals of the tournament in Uruguay on Thursday morning as they bid to become the first New Zealand side to make a FIFA world cup final.
The Oceania champions will go into the match against Spain as significant underdogs.
The European champions won their fourth UEFA U-17 Championship in May when they beat defending champions Germany 2-0 in the final.
Spain defeated the Democratic People's Republic of Korea on penalties in their quarterfinal while New Zealand beat Japan.
Birnie said the New Zealand team have absolute belief they can upset Spain.
"Dare to dream that is what we have been saying to this group for a long time, well before we got over here," said Birnie from Montevideo.
"They are a confident side now and they have it in their heads now and they realise they can compete with anyone. We have shown that. As a staff, we have told them yes it is going to be tough, Spain are a really great side, but so were Japan.
"We were very good in that game in patches and then we showed the true Kiwi fight and grit, and were able to stay in that game in the second half. I don't expect anything different in the Spain game."
Birnie said it hasn't been hard keeping his players grounded as they have toppled bigger nations Finland, Uruguay and Japan throughout the tournament.
"It is hard to get your head around the fact that if we win this match we are into the World Cup final. It is crazy for all involved. But we have tried to normalise every day and every game.
"The players are very well grounded, it is in their nature as people. We have enjoyed the night of the wins and then we have refocused and go again. The girls have been really professional and that is really rewarding as a coach."
Seventeen out of the 21 players selected for this NZ squad had never been to a FIFA Age Group World Cup before and Birnie has been impressed by the way they have handled the occasion.
"The experience of the players who have been in the NZ U-20s and previous World Cups is a big help.
"In the tough times out on the field and there have been plenty, they are the players who have stood up. For the girls who are playing in their first World Cup they have delivered some really big performances. There is maturity in this group beyond their years. That has added to us being able to compete and get results and get so far into the tournament."