CRJ-200 Captain reported the aircraft had an inoperative pack and during initial climb; the aircraft would not pressurize; leading to the flight crew performing an air turnback. The Captain stated the service door was serviced by Maintenance right before the flight.

Narrative

The aircraft had a deferred pack and we were conducting single pack operations. On climbing out on the SID passing through about 9;200 ft. MSL; we received a CABIN ALT caution message. I reduced our climb rate to less than 500 FPM and transferred controls to the FO (First Officer). I checked the ECS (Environmental Control System) page. The right; good pack was pressurized. I began to run the QRH for CABIN ALT Caution when we received the CABIN ALT warning message at close to 11;000 ft. MSL. I instructed the FO / pilot flying to level off and request 10;000 ft. or lower for a pressurization issue. The FO did so and handed me her QRC for CABIN ALT WARNING MESSAGE or EMERGENCY DESCENT PROCEDURE. The procedure called for donning crew oxygen masks and initiating an emergency descent to 10;000 ft. MSL; or lowest safe altitude. I weighed the risks / benefits of donning the oxygen masks; which can restrict visibility and make communication less clear; vs. our close proximity to 10;000 ft. MSL; and high AOV (Air Traffic Safety Oversight Service) in Class B at 5;000 ft. AGL; near ZZZ; and decided not to don masks nor declare an emergency. We notified ATC we needed 10;000 ft. or lower and were going to return to field. I notified the FA (Flight Attendant); passengers; and Dispatch. We conducted Descent and Landing checklists; and landed normally; within weight limits. We taxied to the gate; contacted Maintenance; and in coordination with Operations deplaned and moved the flight to a different plane at a different gate. We briefed taking care not to overpressurize our single pack during takeoff; climb; and possible APU to engine bleed transfer per MEL notes; but did not brief taking our rate of climb and monitoring cabin altitude into consideration. The rate of climb was quite good; 2;500 FPM?; as we were light; and the cabin altitude started at about 5;000 ft. on the ground at ZZZ. That is not far from the CABIN ALT Caution trigger of 8;500 - 10;000 ft. and warning trigger of 10;000 ft. The Service Door had a deferral indicating not closed and had additionally been serviced by Maintenance just prior to our flight for misaligned door closed confirmation witness marks. The FA did not report any unusual sounds from the door during flight.Consider adding a note to the deferred pack MEL to monitor aircraft and cabin alt rate of climb during climb out; and reduce climb rate if cabin alt is rising quickly.