The Socceroos can secure a place in the knockout stage at Qatar 2022 with victory over Denmark in their final Group D game on Wednesday.
Barring a surprise win for Tunisia over reigning champions France, a draw would even suffice.
Australia have not qualified from their group at a World Cup since 2006 and, after Saturday's 1-0 win over Tunisia generated huge excitement, Arnold feels there is now a big opportunity for football Down Under.
The Australian footballing landscape is dominated by Aussie Rules and the two rugby codes but, while those sports are strong in certain parts of the country, they are weaker in others.
Speaking at his pre-match press conference, Arnold said: "Something that's been proven right is that there's one football team, sporting team, that unites the nation and it's the Socceroos.
"When you look at the celebrations in Federation Square down in Melbourne and I've had a few mates send videos of how crazy the place is going, it just shows you that football is alive and well in Australia.
"Putting smiles on Australian faces once is not enough, let's do it some more times. To leave a legacy is huge. It's about putting the game on the map a bit more in Australia."
Arnold, however, recognises the task is far from straightforward.
Denmark, despite failing to win either of their opening two games, still retain hope of qualifying themselves.
Arnold said: "They're a strong team. They are ranked number 10 in the world for a reason. They have been a top team throughout Europe for a long, long time."
France, with six points, have already qualified from the group. Australia are second on three points, with Tunisia and Denmark having one each.
Denmark have no room for error but coach Kasper Hjulmand believes the contest at the Al Janoub Stadium will be an open one.
Hjulmand said: "Australia don't really know if they'll progress with a draw so I think they will come out very strong.
"I definitely expect them to attack and run at us. There'll be times where we have to break down a very strong defensive unit.
"My thinking is to prepare the team to play well and win the match. We are practising and training well and focusing on the task at hand."
An extra complication for Hjulmand could be what is happening in the game between Tunisia and France.
But he said: "I don't have the brain capacity to think about that match - all that is on my mind is this game and preparing my boys to try to win.
"We'll be monitoring, that's for sure, but we are playing to win and hopefully that will be enough."