Murray, 33, is aiming to compete in a Grand Slam for the first time since January 2019 at the US and French Opens in the next few months.
The Scot had career-saving hip surgery in 2019, before his latest long-term injury layoff due to a pelvic injury.
Murray showed plenty of signs of rustiness, but was still too good for world number 211 Liam Broady to win 6-2, 6-2 at the National Tennis Centre in Roehampton.
“Rightfully so,” said Murray of his low expectations. “I’ve had many injury problems, I’m very slow now so not expecting much.
“For a first match in seven months, I have not been practising that much, I have not been doing that well in practice matches, it was alright.”
Next up Murray faces British number two Kyle Edmund on Wednesday.
“I’d be surprised if I manage to come through that one,” added Murray.