The former world No1 beat Benoit Paire in straight sets to set up a second-round encounter against No1 seed Matteo Berrettini tomorrow.
Murray said he had come out relatively unscathed from a little over an hour on court, insisting there were no issues with his hip, although he felt twinges in his groin during the course of the match.
Looking ahead to Berrettini, the three-time Grand Slam champion said he would need to "raise his game to another level" compared to facing an unfocused Paire.
"The match wasn't particularly taxing," said Murray. "Physically, there weren't a lot of long rallies. I had to run up to quite a lot of drop-shots and stuff, so there was a change of direction, which was good."
Murray said that in the past he had been plagued on court by pain to the extent that "it has been too much that I have not just been able to play through it".
There was a slight scare when he slipped and fell during his second service game against Paire, but the Scot gave himself a clean bill of health afterwards. "Although I had some discomfort in the groin, it was manageable and did not affect my performance," he said.
A host of Brits have been given wildcards for the Championships, which start on June 28, including Fran Jones, who has three fingers and a thumb on each hand and seven toes. She defied her disability to qualify for the Australian Open at the start of the year.
Other British wildcards include Jack Draper, who is in action at Queen's today, Liam Broady, Jay Clarke, Katie Boulter, Harriet Dart, Jodie Burrage and Samantha Murray Sharan.