World champions Australia managed a meagre 214 all out at The Oval on Wednesday, all-rounder Maxwell top-scoring with 62.
England, however, then suffered a collapse of their own before stuttering to a three-wicket win with six overs to spare.
Australia are missing several key players, with star batsmen Steve Smith and David Warner serving year-long bans for their roles in March's ball-tampering scandal in Cape Town, while Ashes-winning fast bowlers Mitchell Starc, Pat Cummins and Josh Hazlewood are all injured.
And Maxwell was particularly heartened by their bowling display at The Oval ahead of Saturday's second ODI in Cardiff.
"To be able to push England as far as we did with such a below-par total gives us a lot of confidence," he told reporters at Cardiff's Sophia Gardens ground on Friday.
"We couldn't have batted much worse, but we still gave ourselves a chance at the end."
As for his own batting performance in London, he added: "I left 13 or 14 overs out there.
"But having said that, I felt I hit the ball well and stuck to my strengths.
"I hope it is a building block for the rest of the tournament. It's a start.
"But the team is looking for big hundreds and match-winning scores -- and 60s are not match-winning scores."
Maxwell had a spell in the international wilderness while Smith was skipper, but is now looking to give himself every chance to stay in the side.
"I've continued to train as hard as I can, try to be the number one trainer for everyone else to aspire to," he said.
"If I can continue to lead the way on the training track, then I hope that leads to results on the field," Maxwell added.