A320 Captain reported safely returning to departure airport after experiencing a problem with a pack that led to a loss of cabin pressure.

Narrative

On Day 0; an abnormal situation occurred during flight ABCD.Situation:Everything was carried out without anomalies during the initial climb; ATC instructed us to climb and maintain FL270. Our final cruising level was FL370.Once level at FL270; an ECAM CAUTION 'AIR PACK 1 REGUL FAULT' appeared; showing on the ECAM SD BLEED PAGE both PACKS in amber and position CLOSED. I assessed for a few seconds the condition of the PACK FLOW VALVES and verified on the OVERHEAD PANEL if there was any light on the pushbutton switch related to the current system status; I noticed that the information presented did not correspond to the associated ECAM.An OEB (Operations Engineering Bulletin) was mentioned and recalled; and it was discussed between both pilots that the ECAM entry did not correspond to our situation; so a possible application of said OEB was dismissed. As part of my analysis; I verified the status of CAB ALT and CAB V/S; which apparently was increasing at 900 ft/min and a cabin altitude of 5;450 ft.Actions:A few seconds later; ATC instructed us to continue the climb; to which we requested to maintain FL270. I decided to call the flight attendants normally to inform them that we were facing a possible depressurization and that they should remain seated.I determined that for safety we had to descend to 13;000 ft; an altitude previously identified during the threat management phase in the BRIEFING. Initially; descent to FL190 was authorized.During the descent between FL270 and FL190; there was an abrupt increase in CAB V/S and CAB ALT; reaching and exceeding 9;550 ft of CAB ALT; so the EMER DESCENT procedure was applied in accordance with the manual. Priority handling was requested with ATC.ATC instructed us to descend to 13;000 ft and gave an initial heading toward ZZZ; which I identified as meeting minimum obstacle clearance altitudes and confirmed that the AFS (Autoflight System) was complying with the ATC instruction.Once established in descent; the ECAM action lines were initiated.It is important to mention that the CAB ALT showed a positive trend and close to 14;000 ft CAB ALT; so the MASKS MAN ON pushbutton switch was pressed in accordance with manual/EMER DESCENT.Upon reaching 10;000 ft MSL; the First Officer removed his oxygen mask; followed by me.Due to weather conditions; operational benefits; emergency service support; and commercial and Dispatch advantages; the conscious decision was made to return to ZZZ.I told my purser that we were already at 10;000 ft; that everything was under control; and that we were returning to ZZZ with an estimated 15 minutes. In addition to notifying her of those elements; I asked about the passengers' status and added that I would make an announcement regarding what had happened and the next steps.This passenger announcement was made once the decision had been taken; emphasizing the following points:Everything is under control.We are returning to ZZZ.Estimated 15 minutes to landing.Please follow the instructions of our flight attendants.Already flying toward ZZZ; I took into account the crew's well-being. In particular; my First Officer was in good condition to begin the instrument approach to Runway XXL. I decided to transfer controls to prepare the FMGC and ensured that APPROACH C/L had been completed.We noticed that ZZZ Approach expedited other traffic to give us priority; however; I decided to notify them that we were no longer in a priority situation so that we could continue a normal approach and thus manage our workload.During final approach; we received a call from the cabin crew. Given the nature of the situation; I decided to authorize the First Officer to answer it; anticipating a possible medical situation and being in time to make the request to ATC.Medical assistance was requested upon confirming that the call was due to an infant who was unconscious.Result:The landing was carried out without incident.After landing; police services escorted us to gate XX; and upon opening the aircraft door; they entered to ensure everything was under control.A passenger announcement was made prioritizing the following points:Reason for the return.Situation under control at all times.Message of calm.Appreciation for patience and cooperation.