Marsh posted his highest ODI score for Australia with a stellar 151 in the 200-run win over Scotland in Edinburgh on Tuesday.
It was only the second ODI appearance since October, 2011 for a player who has drifted in and out of the national limited-overs teams.
Marsh's Test career has been similarly frustrating.
After scoring 141 on debut against Sri Lanka in 2011, a disastrous series against India two months later meant his stint was short-lived.
QUICK SINGLE: Marsh, Finch fire for Australia
The 30-year-old admits he'd love another crack at Test cricket in the return Ashes series in Australia later this year.
But he has a more pressing focus in the five-match ODI series against England, starting on Friday.
"To be honest, I'm not thinking about it (the Ashes)," Marsh said after combining with Aaron Finch for an Australian-record first-wicket partnership of 246 in Edinburgh.
"I'm just trying to cement my place in the one-day team first and I've got a great opportunity to do that over the next five games.
"If I score runs, we'll see what happens.
"I'm feeling good with my game. I've played well over the last few months with Australia A.
"I feel ready now. I've just got to keep working hard, keep being nice and patient out there and I'm looking forward to this challenge."
David Warner's omission from the one-day squad means Marsh and Finch will get the chance to further develop their partnership in coming games.
With Shane Watson used at first drop, as he was in the fifth Ashes Test at The Oval, Australia will look to their top order to take the game to England with early aggression.
"We're all powerful hitters," Marsh said.
"If we can get out there and be positive against England, it'll put us in good stead I reckon."