Newly adopted cat won't go pee

We just adopt a 8 month old cat last night. He is a really nice and calm baby. We put him in a small guest room cause our dog is too excited to see him. New baby has eat and drink water. But no sign of bathroom yet... I'm a little bit worried. The litter we bought is different than the one he used I the shelter.. Hope he will pee or poop soon... Is anyone can let me know how long should I wait until he goes to bathroom? And should I bring him to the vet?

Thank you all

when I first adopted my cat Binx he didn't go to the bathroom for about 2&a half days he was comfortable cuddly and seemed happy but I'm sure he was stressed. Usually cats/kittens refrain from eating and using the bathroom when stressed just give it a couple days just give it a couple days

We saved a feral kitten once, and it took him a few days to potty.