Incredibly, there was another level of noise for the crowd of over 75,000 at the Olympic Stadium to reach. The loudest roar of the night came when Australia were already through. Leading Denmark by two goals, the Women’s World Cup and its co-hosts got the moment they had been waiting for. Sam Kerr, the face of the tournament, had finally arrived. Ruled out of the group stages due to injury, Kerr got her first minutes of the World Cup as the Matildas stood with one foot already in the quarter-finals. With the game won and Denmark well beaten, Kerr’s touches were inconsequential; that her only shot from the angle flashed over the bar did not matter. But Australia have their star back, the final piece for a team who are delivering for their country and are growing with the competition. Kerr’s introduction came moments after Hayley Raso had sent the home crowd into a frenzy, doubling Australia’s lead with a crisp finish from another clinical counter-attack. The crowd in Sydney had been electric when Australia attacked, a rolling wave of noise that grew from Caitlin Foord’s sublime opening goal. Nothing, though, could compare to the welcome Kerr received and what it represented for a team who are starting to believe they are contenders again. For so long at this World Cup, Kerr had been forced to watch on as a kind of mascot: the star who could not play. A calf injury had cruelly ruled the Chelsea star out of Australia’s opening game, an absence that grew to three matches as the Matildas were forced to find a way to survive the group stage without their leader. But Australia’s performance in thrashing Canada 4-0 also ensured that Kerr did not need to be used. Once again without Kerr, this time in the last-16, their display against Denmark meant the game was won when she finally arrived. Because with Kerr sidelined, Australia have managed to adjust, instead becoming a different side entirely. It clicked against Canada, a 4-0 win that not only saved their World Cup but sparked their tournament into life. Players who looked lost without Kerr were suddenly released, and they have now grown with the responsibility. Foord was outstanding once again against Denmark, a constant, driving threat on Australia’s left. She was released for the opening goal by the brilliant Mary Fowler, the 20-year-old who excelled as she manipulated the space between the lines, while Raso scored again with another clinical finish. Suddenly Australia now have goal threats across the front line, with the best striker in the world still to add against either France or Morocco in the quarter-finals. “It’s the icing on the cake,” beamed the Australia manager Tony Gustavsson, but Kerr also returns to a team who have changed in her absence and where actually she isn’t guaranteed a start in the quarter-final given how the side has performed. Australia now have multiple goalscorers and other players have taken some of the weight off her shoulders. “It’s a massive boost,” Foord said. “For other teams looking ahead, it’s pretty scary for them that she’s back with us.” The question now, though, is how and when Kerr returns to the starting line-up, and who drops out. Without Kerr, Australia have settled on a 4-4-2 system that is devastating on the counter-attack, an unassuming loaded gun of formation that is built to spring into life on the break. In the atmosphere of the Olympic Stadium, this sort of gritty, counter-punching team, willed on by a wall of sound, looks so dangerous. Foord fits it superbly. A forward with guts and spirit and as well as skill, who has found her confidence since her underwhelming opening displays against Ireland and Nigeria, she was Australia’s player of the match for the second match in a row. She was released by Fowler’s stunning turn and pass for the opener: Foord, with so much time in which to find the finish, kept her head to bury the shot through the legs of Lene Christensen. Australia’s second was also played out to the soundtrack of a team crashing forwards. The break developed on the left, with Kyra Cooney-Cross’ overlapping run from midfield. Emily van Egmond laid it back to Raso, a player who has found her scoring touch. The finish was fired low into the corner for her third goal of the World Cup. Kerr had called to warm-up only a couple of minutes earlier, the excitement rippling around the stadium, yet Australia did not need her really. This was a composed and confident performance, entirely measured, and avoiding the sort of draining emotional energy that accompanied England’s penalty shootout victory over Nigeria earlier in the day. Denmark barely threatened after going behind. Their early chances invariably came through Pernille Harder, their roaming menace who Denmark are just unable to support. Harder went through twice in the opening stages - driving at a retreating Australia defence, first she went to the outside and shot wide, before then ducking inside and firing straight at Mackenzie Arnold. On both counts she knew she should have done better. Denmark were largely forgotten about here as the hosts cruised through and the Kerr mystery was solved. The theories that the extent of Kerr’s injury was being covered up would have grown when she only watched on during Australia’s warm-up, wearing her boots but wrapped under a heavy coat that did not come off. At half time she was not among the players loosening up on the pitch. But for Australia, getting Kerr back was the final step of a tournament that has been defined by their reaction to overcome challenges. After the chaos of the group stage, where they stood on the brink of an early exit, there was finally a comfortable win. This is a team who are galvanised, coming together, and just at the right time. Read More England survive penalty drama to reveal vital quality in Women’s World Cup dream Who and when do England play next? Lionesses route to the World Cup final Women’s World Cup TV schedule: How to watch every match today Chloe Kelly: England’s woman for the biggest occasion strikes again A timeline of Donald Trump’s spat with Megan Rapinoe How many games will Lauren James miss at Women’s World Cup after red card?