Date: 201912
Local time of day: 0001-0600
Location: ZZZ.TRACON, US
Aircraft: B737-800
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
Airspace: Class E ZZZ
ATC / advisory: TRACON ZZZ
Aircraft component: Pressurization System
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Second reporter function: First Officer; Pilot Not Flying
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft Other Automation
When detected: In-flight
Result: Aircraft Equipment Problem Dissipated; Flight Crew Landed in Emergency Condition; Flight Crew Returned To Departure Airport
Contributing factors: Aircraft; Human Factors
Primary problem: Ambiguous

Narrative: I was the Captain operating flight from ZZZ to ZZZ1. This was day two of a three day for me and due to reassignment my original FO (First Officer) was not on the trip on this day. This was mine and the FO's first leg together. Everything was normal with preflight. The aircraft was towed up to the gate by Ground Personnel about an hour before departure and preparation was normal. I was expecting RWY XXL for takeoff; but when we called for taxi we were assigned RWY XY. FO accomplished the Before Taxi checklist and as we were taxiing out the Before Takeoff checklist was accomplished. We believe we checked everything and did the checklist in accordance with company procedures. Takeoff and climbout were normal. I was the PF (Pilot Flying) and was hand flying the aircraft until the [situation]. Passing 10;000 feet. I chimed the flight attendants as we continued climbing. Passing through approximately 12;500 feet. the Cabin Altitude warning illuminated and the aural horn came on. We donned our oxygen masks and told Center controller we were leveling at 13;000 feet. I then instructed FO to tell Center we needed a descent to 10;000 feet. The only light either of us ever saw was the red Cab Alt light. The FO got the QRH out and started the checklist. We were cleared to descend to 8;000 feet and the light extinguished at some point passing below 10;000 feet. The cabin altitude showed approximately 10;800 feet at the highest. The passenger oxygen masks did not deploy. We returned to ZZZ and landed on RWY XY. Taxi in and shutdown was normal. After we landed we discussed the event and I asked the FO if the switches on the Engine Bleeds; Packs and Crossfeeds we're out of position. He stated he couldn't remember (nor could I); but he thought they were. We both felt certain they were correctly positioned; but the more we questioned ourselves we both admitted we were not 100% certain.My thoughts are that we were not complacent in our preparation nor in accomplishing the checklists; nor were we rushed or distracted; but it is possible that the switches were in the incorrect position on takeoff and got positioned correctly during the [situation] and we simply don't recall either one of us moving them. Neither of us noticed any pressure surges before; during or after. It's possible they occurred and due to the warning horn and mask usage we didn't notice. I should have done a better job of instructing the FO not to touch anything prior to following the steps in the QRH. Also; it took us a while to get the warning horn off; which combined with using the oxygen masks and communicating with ATC and the flight attendants was distracting. Also; since I was hand flying the aircraft when the [situation] occurred; I wish I had immediately gotten the autopilot on. I would have been able to observe and manage the situation in a better way. After landing I asked him if he checked the pressurization per the After Takeoff checklist and he said he's not sure. We certainly have checklists that; if followed correctly; would/should trap these errors. I felt totally comfortable right up to the instant the warning horn and light came on. We weren't rushed; I was well rested and alert. I always make sure that when challenged with 'AC and Bleeds' during the Before Takeoff checklist that I physically point to the Pack AND Engine Bleed switches; making sure they are correctly positioned before I respond 'Auto and Set'. It's possible that the switches were in the incorrect position and that I looked; but didn't notice. I thought I was always diligent in doing this; but as I write this; I wonder if I saw what I wanted to see rather than where the switches actually were. I honestly am not 100% sure.Maintenance checked the aircraft thoroughly; including a pressure check; and found no discrepancies. The aircraft logbook was signed off and we were scheduled to continue our sequence to ZZZ1. I discussed with the FO that we needed to have our minds totally on the current flight and offered to take him off the trip and assured him there would be no repercussions if he felt he would be distracted while continuing the flight. He assured me he was fine; as was I. I briefed the FO that we would NOT discuss this event at all during our flight to ZZZ1 and I asked him if he felt good and able to fly. He responded that he felt good. We both elected to continue on to ZZZ1. I have told you exactly what happened to the absolute best of my ability. I instructed the FO to put in his own words what we experienced and what he thinks happened.Going forward; my intent is to get the autopilot on sooner. Also; I felt like it could have been better run if I had transferred control to him and I had run the QRH; notified ATC; Dispatch; the Flight Attendants and such. It all got completed; just could have been smoother. I hadn't thought about silencing the Cabin Altitude Warning horn in a long time. Today was a reminder that on any given day. Going forward; I'm doubling my effort to verify checklist items; expect the unexpected and follow all checklists precisely; brush up on all systems and to more fluidly and smoothly transition into the situation. I can assure that this will not happen again.


Second narrative: [Report narrative contained no additional information.]


Synopsis: B737-800 flight Crew reported a cabin pressurization malfunction during climb that resulted in a return to the departure airport and uneventful landing.