B737 Pilot reported a pressurization problem with the aircraft during climb and returned for a precautionary landing.

Narrative

We did a 28k; bleeds off takeoff; out of ZZZ. After climb out; my Captain reset the bleeds by the checklist. We continued our climb. Around 28;000'; my Captain noticed the cabin altitude was at 10;000' so we leveled off at 28;000'; saw it was still climbing and started a descent after letting ATC know. By the time we got to 27;000; the cabin alt warning went off. We donned our O2 masks and established communication. My Captain started doing all his tasks; and I started a priority descent; being vectored by ATC towards ZZZZ1. Once passing through 10;000' we removed our masks; and continued through all the checklists; and calls to dispatch; and the FA's; etc etc. Once the Captain had caught up with those duties; we turned back inbound on the approach to Runway XX at ZZZZ1; where we performed and overweight landing. CFR (Crash Fire Rescue) checked our brakes for temp; and we proceed to the gate. We were familiar with the bleeds off takeoff; having performed it 2 days prior. Upon thinking back afterward; when the Captain did the bleeds reset; he remembered that the bleed pressures did not come back up when reset. I did not see the pressures because I was hand flying at the time. The Captain had also just come off X months of leave and was his first trip back flying. It was also a very long day; 3 legs; previous leg had 2 plane swaps; delaying us; and putting us just a few minutes shy of a max 13 hr duty day. I should have been watching more closely when he changed bleeds and I might have caught it.