Cats often hide close by. Check with all your neighbors, around the block & across the street. Knock on doors, and/or distribute notes or fliers with picture & contact info (I printed them 4 to a page, cut up & taped them to front doors). Last year my old cat went missing for 10 days; turns out she was trapped in a neighbor’s garage only two doors away! Your pet is very likely nearby. You may even try putting the litter box or bedding outside, so your cat can smell it. Also, keep checking with nearby vets, and your local shelters (I left or emailed picture-fliers there too). Check daily! Best of luck.
If he is indoor only I will add steps. Need to crack open the garage door or other access 24/7 to let him come back inside ASAP. Definitely close by and I’m sure has taken cover for warmth under a shed or crawl space for example. Need to get fliers. They always try to return to the exit they went usually and night and especially between 4-7 am. Keep an eye on that door and focus on luring with soft familiar calls from that door as often as possible. If you have an attached garage crack that just a bit with scent items inside and just outside both doors (garage and door he went out). Scent items are worn clothes of family, his bedding, your slept on sheets, litter box etc. They can hide so well nearby that it seems as though they have vanished. It’s a way of protecting themselves. Flier door to door in a 7 house radius of your home. That’s typically where they stay for quite some time. Even months. Baby monitor outside the door he escaped is always helpful to hear meows or scratching. Also see site for steps to finding an indoor only cat. There are also steps to outdoor access. Pet-trackerinc.org
Cats are amazing survivors so don't get discouraged. The GOOD NEWS is that unlike dogs, cats normally do not roam very far from home ... WITHIN a 5-7 house radius. Your cat is probably scared, but hiding nearby. Just know that after being outdoors for awhile, an INDOOR cat will go into a protective SURVIVAL mode and will probably NOT respond to YOUR calls ... even if nearby.
If you have a GARAGE, leave the garage door slightly OPEN so your fur baby can have safe access to return home. Place items with your kitty's scent along with STINKY wet food (tuna/sardines) and WATER inside the garage to help lure your kitty. If NO garage, try to leave those above items outside NEAR the door where your kitty EXITED your home.
Cats feel safest to come out of hiding when it's QUIET and DARK. One suggestion would be to walk around your neighborhood at night (between 10 pm - 2 am) shining a FLASHLIGHT and look for reflecting EYES ... beneath cars, bushes, decks and on people's doorsteps. As you walk with the flashlight, call softly for your kitty and SHAKE your car keys or cat treat bag ... a sound that your cat will recognize. It took thirty (30) days to find and rescue my friend's cat. She was hiding in the STORMDRAINS during the day and coming out at night. It just took forever to get any sightings of her.
Please ask your neighbors to CHECK inside/under their BACKYARD SHEDS, decks as well as their GARAGES. Cats have been known to get LOCKED inside a shed/garage after owners finish yardwork.
Also visit your nearby animal shelters IN PERSON. Don't just call as your kitty may be overlooked by the busy staff, so actually go there. I recommend visiting EVERY OTHER DAY, because after the required holding period, the shelter can legally adopt her out or worse (if injured/sick).
I hope and pray that your sweet kitty finds its way back to you. Please keep us posted.