“I hate to sound cliché,” Mr. Stewart said, “but some people have it, and it was so apparent from the tape we had on Jessica. I can’t even talk about it without going into my old Jewish man agent voice. She made great choices, surprising choices. Thirty seconds in, we were trying to figure out how to get in touch with her. We couldn’t believe it when we found out she was still in school!”

During her “Daily Show” tenure, Ms. Williams helped create the WNYC podcast “2 Dope Queens,” on which she and Phoebe Robinson, her friend and a fellow comedian, swap stories and host performers, with an emphasis on women, minority and L.G.B.T.Q. guests.

“We try to make sure we’re the stars of our own narratives,” Ms. Williams explained.

It’s a maxim she tries to apply to the film and television roles she seeks out, and those she does not pursue. Though fans expressed some disappointment when she said she did not want to be considered for Mr. Stewart’s job when he left “The Daily Show” in 2015, Ms. Williams said it was an easy decision.

“I know what I’d be incredible at, and I know what I wouldn’t be as great at,” she explained. “I didn’t want to insert myself into that narrative to please everybody else. I was listening to my heart and making sure I honored what I was truly excellent at.”

Ms. Robinson said Ms. Williams has been careful to step back and assess the bigger picture at moments when expectations can feel overwhelming.

“I can’t even imagine dealing with all this attention on her — wondering if people really want to be her friend or if they just want access to Jon Stewart,” Ms. Robinson said.