Federer beat Sousa 6-4, 6-3 this morning almost 24 hours after the match was initially due to take place.
Rain plagued Rome yesterday meaning tournament organisers had to deal with severe fixture congestion.
Swiss star Federer was the first ATP match to take place on centre court this morning.
And he made light work of Sousa to ensure he was fresh for his second match of the day against Borna Coric.
However, the 20-time Grand Slam winner questioned if the result would have been the same if they had started their match in the rain.
“So far so good,” Federer said.
“I think yesterday would have been completely different conditions.
“I don’t know if the score would have been different but from that stand point I am happy.
“We got to play a good match.
“It is a slippery court here and it is tough to play.
“Every clay court plays slightly different and I think when it is nicer weather it slides a lot.
“I came out of the blocks well and I had a good feeling.
“I didn’t get broken on clay in the first round which is a good sign.”
Federer will be moved to court Grandstand later this evening when he takes on Coric.
The match is due to get underway around 5pm (BST).