No sleep

My almost 6 month old keeps waking up every 2-3 hrs at night and his day naps are 2-3 of 30 mins long naps. If we’re lucky he’ll sleep for 1 hr. Most of the time he won’t stay in his crib after 3 am. I refused to do the cry it out method but last night was bad and I had to leave him crying in his crib for some time bc I felt very irritated. He didn’t go to sleep until 5:30. I make sure he gets his calories in during the day, we have a routine for nighttime.. bath, night bottle, white noise, paci, red night lamp and he still wakes up often. Any recommendations?