my cat brought in a baby squirrel tonight

He seems uninjured, furry, actively seeking skin contact, hasn't opened his eyes but moves to hold on when i put him back in his box. i have him in a box of soft cloths with a warm water bottle next to him, and I've given him about 1 ml of pedialyte with a syringe, drop by drop so far.

looking for ALL advice but specifically on whether and how to try and reunite this guy with his mom. problems are:
1. my cat brought him in so i have no idea where the nest is
2. its night time and all I've read says his mom won't be active at night or willing to come look for him on the ground.

with limited time to take care of him myself... should i spend an hour putting him outside tomorrow morning (and how would you advise setting him up so she comes looking) or should I just take him to a wildlife rehab center asap (the audubon society is closest here in portland i think).

thank you for the help! he's so cute and i want him to make it and lead a happy wild squirrel life