The Matildas have left Denmark to go their separate ways: the staff and a couple of players halfway round the world to Australia, two over the Atlantic to the US, the rest making shorter trips to England and Sweden

What they all had in common was a renewed belief in the process.

For months, coach Tony Gustavsson has insisted Australia's women's soccer team was on course to challenge for next year's home-hosted World Cup.

He had even admitted to watching England win this year's European Championship at home under a foreign coach and dreamed of what might be.

But results had stubbornly refused to back him, and the external noise was growing loud enough to threaten the internal calm.

Back-to-back victories in Europe have changed the mood.

South Africa, beaten 4-1 in London on Saturday, were weak opposition, but Tuesday's 3-1 win over a much stronger Danish side in Viborg was a statement success.

It was Australia's first victory against European opposition in Europe since beating Finland in Cyprus in 2015, and their first on opposition territory since defeating France in Angers in 2013.

Gustavsson and Football Australia had chosen a pathway of playing top-10 sides including United States, Canada and Spain, all of whom beat the Matildas, "to give us the chance to perform at the World Cup", assistant coach Mel Andreatta said after the game.

"Internally we really believed in it and I hope now externally, after two good wins, people will see we are on the right trajectory going into World Cup 2023," she said.

The other part of the process has been developing the greater depth required in tournaments by bringing in young players.

This was rewarded as the likes of Kyra Cooney-Cross (20), Charlotte Grant (21) and Alex Chidiac (23) all shone in the absence of injured senior players, along with Saturday's two-goal star Cortnee Vine (24).

"There's been a lot of work on depth and we're starting to see the fruits of it," Andreatta said.

"Chidiac was a game-changer off the bench, Cortnee Vine again gave a solid performance ... it has created competition for spots, raised the level of training and been really beneficial for the whole group."

The Matildas next play at home in November, when they will face Sweden in Melbourne and Thailand in Sydney with their belief in the process restored and reinforced.