Scotland are looking to halt a seven-match losing run when they take on the Wallabies in Newcastle on June 5.
Andy Robinson's men then take on Fiji and Samoa, with positive results imperative after following up their first failure to qualify for the World Cup quarter-finals with an RBS 6 Nations wooden spoon.
Scottish rugby has had more favourable results since then, with Edinburgh reaching the Heineken Cup semi-finals and Glasgow involved in the RaboDirect Pro12 play-offs.
And the naturally positive Cross is full of confidence that their Australasian tour can reverse the recent trend for the international team.
The Edinburgh forward told Press Association Sport: "It's very exciting because we have got some new challenges ahead of us.
"I think this is going to be a really exciting tour, something we can enjoy.
"I believe there is the very real possibility that if we play as we can then it can be three wins from three and we are preparing for that.
"What we've got to do is work on our strengths and take that consistency we are going to develop in training and use it in the games.
"If we can take the consistency of performance we have shown in training into games I believe we can beat anyone.
"I believe if we play as well as we can, we can beat any team in world rugby.
"The challenge for us is to play as well as we can consistently.
"We haven't done that in the past and that's why we haven't been winning the games that we've lost."
Scotland's previous summer tour resulted in Robinson's best times in the job, winning both matches in Argentina.
Cross was part of that squad and is looking forward to the challenge of repeating that success.
"I believe winning comes from performing basic skills consistently under pressure," Cross said.
"We did that out there and it showed we can win against world-class opposition. The Argentinians are a very good rugby team and are improving.
"We have been out there on our previous southern hemisphere tour and got our first series victory down there.
"Because you travel away so far from home and you're together for such a long time, it is a great chance to spend time with the guys and build relationships on and off the pitch so you can facilitate your performance for Scotland.
"But there are games to win and we're professional rugby players and that's the first mandate in the job description."
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