"It's just an wonderful feeling".
Two matches have been left unfinished at the French Open as play was suspended Sunday night because of darkness.
The ninth-seeded Williams has struggled on clay this season and that continued in a 6-4, 7-5 loss on Sunday.
As for Kozlova, she advances to the second round in Paris for the first time, and awaits the victor of Monday's match between Katerina Siniakova and former World No.1 Victoria Azarenka.
Safwat got into the field as a "lucky loser", someone who failed to make it out of the qualifying rounds but is given a berth when another player withdraws.
Australia's Nick Kyrgios also pulled out ahead of Monday's contest with compatriot Bernard Tomic with an elbow injury.
Spain's Rafael Nadal is set to begin his pursuit of an 11th French Open men's singles title against Simone Bolelli of Italy tomorrow.
The world number five never looked at ease on the Roland Garros main show court, slumping to a 7-5 6-3 defeat to a Ukrainian opponent who had won both the pair's previous meetings. Ostapenko became only the sixth female major victor to lose in the opening round of their title defence.More news: USA states declare emergency ahead of subtropical storm
Serbia's Novak Djokovic was also well below his best yesterday after opening his campaign with a 6-3, 6-4, 6-4 victory over Rogerio Dutra Silva yesterday. Konta has yet to win a match in Paris in four appearances.
Venus Williams crashed to a straight-sets defeat in the opening round, losing 6-4 7-5 to China's Qiang Wang on Court Suzanne-Lenglen.
The 23-year-old, who won her second consecutive Italian Open title last weekend, will next play either 2010 champion Francesca Schiavone or Slovakia's Viktoria Kuzmova. "In general I played maybe like 20 per cent of what I can play", said Ostapenko.
"I only heard I was playing an hour before the match", said Safwat. Now we're out here battling on such a court.
"I will just try to forget this as soon as I can". "So you never forget that".
Fellow American Sloane Stephens, seeded 10th, had no problems in her opener, breezing to a 6-2, 6-0 win over Arantxa Rus of Netherlands. The American relentlessly attacked her opponent from the baseline and needed just 49 minutes to wrap up the victory.
Nishikori, a 28-year-old from Japan, is seeded 19th at Roland Garros.
Former semi-finalist Gael Monfils shrugged off a typically sluggish first set to triumph against fellow Frenchman Elliot Benchetrit 3-6, 6-1, 6-2, 6-1.