Murray, ranked 10th but taking the eighth seed due to the injury absences of Rafael Nadal and Juan Martin del Potro, admitted he found himself caught on the hop with his preparation when Nadal withdrew last week from both Toronto and Cincinnati to let a right wrist injury heal.
Murray, who then received a bye into the second round as a top eight seed, had been expecting to play on Monday evening.
The former Wimbledon winner confessed that his new opening date at mid-week has actually thrown off his finely balanced preparation with Mauresmo, whom he signed to a long-term contract in recent days.
"I planned all of my training and everything around playing my first match on Monday evening and arranged to come here Thursday to get here a little bit earlier to get used to the conditions," Murray said.
Murray begins the tournament he won in 2009-2010 against either Santiago Giraldo or Australian Nick Kyrgios, who knocked Nadal out of Wimbledon in the fourth round last month.
The 27-year-old Scot admits he's still trying to find traction after his September back surgery and subsequent return to tennis at the start of this season.
Murray is still seeking his first title since thrilling Britain with his 2013 Wimbledon crown.
He said that he is putting special emphasis on this week and next in Cincinnati, his warm-ups for the US Open that starts on August 25, after a quarter-final loss to Grigor Dimitrov at Wimbledon.
"You don't just come back after surgery and feel great straightaway the first few months," Murray said. "I was happy with the French Open. That went well.
"Wimbledon obviously, not quite as well as I would have liked, although I felt like I played some good tennis before my loss there," he said. "I felt like I was playing pretty well.
"But the rankings don't lie. I need to start winning more matches to push my ranking back up there.
"The main goal for me is to try to win Grand Slams. That's what motivates me. That's why I want to train."
As rain played havoc with the schedule, first-round action got underway.
- Tsonga seeks to regain spirit -
French 13th seed Jo-Wilfried Tsonga finished with his ninth and 10th aces in a 7-6 (7/3), 6-1 defeat of Edouard Roger-Vasselin, his fourth win this season over his compatriot.
Tsonga, who advanced in 75 minutes, saved all three break points he faced as he played for the first time since losing in the Wimbledon fourth round to Novak Djokovic. He lost only two points on first serves.
"Most everything was working, but the first set was not easy," said Tsonga of the 53-minute opener. "He was playing well. I haven't played matches in some weeks, I was happy to go through.
"I've been working on my mental game," said the player who won the last of his 10 career titles 18 months ago. "It can be difficult losing every week.You can get used to it.
"I've tried to get my fighting spirit back."
Ivan Dodig finished with an ace to knock out the first seed of the week as he upset 10th-seeded John Isner 6-4, 6-7 (4/7), 6-3.
Feliciano Lopez beat 14th seed and fellow Spaniard Roberto Bautista Agut 7-6 (9/7), 6-3.
Croatian number 15 Marin Cilic beat Uzbek Denis Istomin 6-2, 4-6, 7-5 while Frenchman Jeremy Chardy reached the second round with his 6-3, 5-7, 6-4 defeat of Argentine Federico Delbonis.
He was joined by compatriot Benoit Paire, a winner over Colombian Alejandro Falla 6-7 (3/7), 6-4, 6-2.
Two Australians lost, with Julien Benneteau defeating Lleyton Hewitt 6-1, 6-2 and South African Kevin Anderson defeating teenaged Thanasi Kokkinakis 4-6, 6-2, 6-3.
- Sports & Recreation
- Andy Murray
- Rafael Nadal
- Amelie Mauresmo