The pair was spotted together at Giorgio Baldi in Santa Monica, Calif., on Sunday, November 21, the Daily Mail reported.
According to photos obtained by the outlet, the King of Staten Island actor and the reality star giggled as they left the restaurant.
The Saturday Night Live star was also spotted with what looked like a hickey on the left side of his neck, the outlet noted.
Kardashian wore black trousers underneath a black leather skirt with a black turtleneck top and a baseball hat. Davidson also wore a baseball hat, which he paired with denim jeans, a green t-shirt and a gray jacket. The pair was spotted walking hand-in-hand.
Davidson seemed flustered by the attention from the press, the outlet noted. Kardashian seemed to be cool and collected in the pictures. The couple burst into laugher once they got into Davidson's car.
"It was just the two of them," an insider told Us Weekly of the date. "They walked straight to the corner table at the end of the restaurant."
"The restaurant kind of went silent when they first walked in, but then no one really paid attention to them," the source explained. The new couple was said to have been "cuddled up" and were "talking very quietly" for most of their meal. At one point it seemed that the 28-year-old "flirtatiously whispered something into her ear" and was "kind of giggly" with Kardashian.
Last week, the Daily Mail obtained photos of the couple holding hands while on a walk together in Palm Springs, Calif.
"They have such a strong connection," an OK! insider previously spilled. "Kim’s going with the flow, but she’s excited about what it could bring."
Another insider told OK! that the SKIMS founder "needed lightness and laughter, which Pete offers in abundance. She’s having a blast and telling people he’s like a breath of fresh air." "Pete’s unlike anyone she’s dated," the source explained. "He has her in stitches but also has an intellectual, deep side. She’s starting to see what all the fuss is about!"