When the draw for the playoffs was made, Wales learned that home victories over Finland and whoever prevailed out of Poland and Estonia would see them qualify for the finals in the summer.
Although Wales were marginal favourites to overcome Thursday's opponents, few would have predicted the manner of their win as they surged to success in Cardiff.
David Brooks set the ball rolling with a goal in the third minute and although Teemu Pukki halved the deficit on half time after Neco Williams had scored a second, Brennan Johnson and Daniel James scored after the break.
With Poland cruising to a 5-1 triumph over Estonia, the two nations will now meet at the Cardiff City Stadium on Tuesday night.
Speaking after the match, Page attempted to find a balance between praising his side's display and insisting that their quest to reach another major finals is only at "half time".
Speaking to S4C, Page said: "We got off the best possible start. We had to address a couple of things at half time and were better in the second half.
"It could have been five or six, but the message is that this is half time. We've now got a massive effort to go on Tuesday and we can't wait.
"We were disappointed with the goal we conceded. It made for an uncomfortable few minutes but the start of the second half was excellent."
Opposite number Markku Kanerva added: "I want to congratulate Wales, they played a good game today and deserved to win.
"Of course I am disappointed, we didn't reach the level I wished. We had disastrous starts to both halves with Wales scoring in both those periods. Hopefully Wales will go all the way to the Euros, because they are a good team."
Wales possess an abysmal record in games against Poland, failing to win since their first-ever game in 1973 and losing their last six encounters in all competitions dating back to 2001.