Mona was a 21st century Human who worked as a waitress in 2024.
She worked at a diner in downtown Los Angeles where Q met Doctor Adam Soong on April 12, 2024. (PIC: "Fly Me to the Moon")
Background information[]

Mona in a deleted scene
Mona was played by actress Jackie Geary.
The character originally had a speaking role and was featured in a scene where Q (waiting for Soong) questioned her about the meaning of her existence. However, the scene ended up deleted from the finished episode and Mona can only be seen in the background as a non-speaking extra.
The deleted scene can be seen on the PIC Season 2 Blu-ray.
Her name, which originated from the name tag she wore, was presumably named after a character Geary played in the 2017 episode "Causality" in Picard showrunner Terry Matalas' earlier science fiction series 12 Monkeys. (citation needed • edit)