The 31-year-old Olympic champion is aiming to become the first woman in history to win 5,000m, 10,000m and marathon gold at the same Olympics, emulating Czech great Emil Zatopek, who achieved the men's triple at the 1952 Helsinki Games.
After spending most of Friday's opening heat at the back of the pack, Hassan coolly accelerated through the field on the final lap to come home second in 14min 57.65sec, a whisker behind Kenyan rival Faith Kipyegon, the two-time Olympic 1,500m champion, who crossed first in 14:57.56.
Another of Hassan's rivals, Ethiopia's 2022 5,000m world champion Gudaf Tsegay, comfortably qualified fifth in 14:57.84.
Hassan's daunting Paris schedule is the latest example of her willingness to test the boundaries of the possible after she tackled the 10,000m, 5,000m and 1,500m at the Tokyo Olympics in 2021.
That effort ultimately fell short -- she won gold in the 5,000m and 10,000m but settled for bronze in the 1,500m -- but Friday's 5,000m performance at the Stade de France indicated she might just have the form to match her ambitions.
Asked afterwards if she believed her treble bid was really possible, Hassan admitted she occasionally doubted herself.
"I haven't finished all three (events)," she said. "I just did the heat and we'll see if it's possible after I complete the marathon, but I think it's possible.
"I have four races -- one has already finished, I have three left. But I'm very nervous for the marathon."
Hassan told reporters her treble attempt was a product of her curious nature.
"Most of the time because I'm a very curious person -- I think the curiosity made me to do this, all of them," she said.
"But when you ask me at home, I always say 'Oh, I'm gonna do five events or four events.'
"But when I'm in the stadium I'm always saying 'Why the hell am I doing this, why did I decide to do this? I shouldn't have done this.'"
Potentially the biggest obstacle to Hassan's treble is Kipyegon, who is aiming to repeat the 1,500m and 5,000m double she completed at last year's World Championships.
Kipyegon said she had revelled in facing Hassan in Friday's opener.
"That was a dream to meet her in the heats and now we'll meet again in the finals," Kipyegon said. "It was a good race.
"It was just good to step on the track and execute as good as possible."
Kipyegon, who could complete a hat-trick of Olympic 1,500m golds in Paris, said she is unfazed by stepping up to the 5,000m in addition to her specialist event.
"Nowadays I like doing both," she said. "It's my first doubling in Olympics and I hope one of them will go well."
