I'm sure he/she is hiding nearby or could have been accidentally locked in a neighbor's garage - talk to all neighbors in a several block radius. Posters are helpful and do notify police and animal shelters..
Most importantly, I would get a chair, a bowl of her/his favorite food or tuna, a used litter box for scent, and stay outside your door in that chair tonight and every night until he/she comes home.
You must monitor the litter box! The scent of litter boxes attracts predators like wild dogs and coyotes and most experts suggest caution. In my advice post I specify that you must remain outside to monitor the litter box. Animals can smell these a mile away and the last thing you want is to lure your kitty into a coyote ambush.
Here’s a recent joyous post discussing a lost kitty who was found: "Thank you all for help in finding Patty! She was found by kind neighbors a street over. She was stuck in a tree. Patty is getting all the love, dinner, fresh water, and all the attention.”
Thank you Patty for reminding us to look in all possible places including high trees and utility poles especially at night. Kitties can climb up a tree or pole to escape from a predator often in the middle of the night when they are active.
Yes, I know it’s cold tonight but so is it cold for your baby – just bring blankets and a warm hat.
Cats hide during the day but will come out late at night when they feel its safe. You need to be there when she/he comes back because he/she will not hang around and wait for you. Be patient and call her/him by name often. This will require some work and inconvenience but it will be well worth the effort.