Commercial Fixed Wing
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Distraction; Time Pressure; Workload
Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Other / Unknown
Air Traffic Control Issued Advisory / Alert
Environment - Non Weather Related; Human Factors
During climbout on a heading of east on the ZZZZZ2 SID while passing 8;000 feet between ZZZZZ and ZZZZZ1 we got a TCAS TA regarding traffic descending off ZZZZZ3 on the ZZZZZ4  flowing south at 1 o'clock; 3-5 miles ahead that was no factor.  This is something we see every day on climb out or descent in and out of ZZZ due to climb and descent rates.   ATC then called traffic at our '10-11 O'clock 3 miles descending to one one (11) thousand I called 'traffic in site no factor; they're passing above and behind us.'  ATC then asked our Altitude.  I replied 'level 10;000 feet.He asked our altitude again; I replied 'Level 10;000 feet; he said he saw us at 10;500 feet and gave us an updated Altimeter setting; and cleared us to climb to 17;000 feet.  Passing 12;000 feet he asked us what altitude we were passing.  I replied '12;000 feet.'  He then replied 'That's what we show as well.  For some reason I had you at 10;500 feet back there. I have a phone number to copy when you are ready.'  We took the number down; and he said 'Call us when you get to your destination to discuss a possible pilot deviation.'The Captain called when we got to ZZZ1.  The Controller Supervisor who answered said he had just sat down; had no idea what we were talking about; said he would do some research and call us back.  5 minutes later he called us back and said; 'After review; the previous Controller showed you slightly high and stopped traffic on the arrival at 12;000 feet (which I thought was at 11;000 based on his advisory call).  Then showed our altitude correct in the climb after he inquired again passing 12;000 feet.  Said there was no conflicts or loss of separation; not a big deal; and that he would just file it as an RA report and close It out; however; we had no known RA's; nor any TA/RA indications for the potential conflicting traffic passing above and behind us?  The ATC Supervisor didn't take any further action or questions; and wished us a safe rest of our day and left It at that.  We thought It would behoove of us to fill out this report regardless.Wrong altimeter setting.  We had a lot of distractions from multiple visitors on the flight deck at the gate while setting up cockpit and during the before start checklist (flight attendants; gate agents; deadheading crew and commuting pilots who we knew who stopped by to visit).  Flight attendants held off boarding passengers who were held up at the door; until catering; who arrived at the aircraft late; had cleared the forward galley and aisle; and got them their snack/sanitary packages set up to hand out.  So this backlogged the jet bridge; had the flight attendants coming in and out of the cockpit along with the commuting pilots; and gave us a lot of distractions.  This back log seemed to frustrate the agent; for It was the flight attendants who were keeping the passengers out of the way until they were ready for them.  For that; the gate agent was rushing to close the flight (We still pushed 10 min early).  The FA A seemed rushed; and just closed the flight deck door before verifying if we were ready or saying 'seated and stowed;' which was nonstandard.  These multiple interruptions (which seem to happen every flight these days) just added up; we had the current ATIS printed off; but when back tracked to get caught up; we missed the altimeter settings; which must have been set from a flight a day or two prior due to the difference in what It actually was at the time.Verify; Verify; Verify; Trap the Errors; Don't let the distractions of the daily operations knock you off your game.  It was a beautiful cold VFR morning; flying with a Captain I had enjoyed flying with in the past; so I felt we were both comfortable and familiar with how each other operates within the SOP's and as a person.  The Aircraft had sat overnight.  I would like to see more operational (non-flying) related distraction/awareness incorporated into training.  The day prior on a separate flight we had a passenger removed by law enforcement for non-compliance/and possible criminal related activity.  Gate agents are constantly under stress to get flights out on time or early.  To top It all off; everyone has been under stress of the pandemic; furlough related; or state of the airline related issues.-"
Air Carrier First Officer reported the pilot crew failed to set the correct altimeter setting causing an altitude deviation. Pre-flight distractions; including the current pandemic situation; were cited for the error.