England have lost the last eight Ashes campaigns but their recent 2-1 Test series win in South Africa followed series victories against West Indies (home and away) and New Zealand.
However, England will have to raise their game further against Ricky Ponting's all-conquering team and Somerset opening batsman Trescothick, returning from South Africa, said: "We've beaten South Africa but how much we have to improve before we face Australia is the million-dollar question.
"We have some time off now to reflect, to improve, get fit and begin work for the summer. We'll be in good shape and ready to go by the time the series arrives."
Tournament hosts England beat Australia in September's Champions Trophy semi-final before losing The Oval climax against the West Indies.
In South Africa, at the end of a long tour, England lost the One-day series 4-1 with the top order in particular struggling.
Left-hander Trescothick could only manage an average of fractionally more than 14 in the Limited Overs Internationals and he added: "It's always going to be tough at the end of the tour. It was a long trip and some of the guys have been out there longer than others. We've all put in a lot of effort so we're all very tired."
However, he said nothing could take the shine off England's first Test series win in South Africa for 40 years.
"The Test matches were the main event. Beating a team as good as South Africa was a major achievement. It was a hard-fought series.
"The One-dayers were very disappointing because we didn't do what we wanted to do. But overall we're pretty pleased."