Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Distraction; Communication Breakdown; Situational Awareness; Training / Qualification
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Chart Or Publication; Human Factors; Procedure; Environment - Non Weather Related
Departure clearance is not received until taxi out; close to departure end of runway. We were flight planned for one SID but given another SID when I received the clearance on taxi out. I remember looking at the SID; which has approximately 6 different SIDS on one page and did not realize the assigned SID was not on the SID page; but depicted on the runway page. Shortly after the clearance was received; there was also a distraction regarding the aircraft. I cannot remember; but it might have been a transient ECAM; this aircraft had several when we left ZZZ. I performed the takeoff and realized then that we did not have the assigned departure. The CA also did not catch the change in SID; and we queried ATC for a verbal description of the departure.I have not flown much in the past 7 months and normally avoid Country X. Due to the language barrier; previous aircraft malfunctions; assigned SID not on SID page and another distraction I cannot specifically remember; I failed to change the SID in the FMS. This is just being reported now because there was not time between this flight and the next leg due to interview to renew customs clearance; being selected for random security check; the need to obtain food prior to flight. The next leg involved an air divert and was more on my mind than this. All published SIDs on one page would greatly enhance situational awareness. Although we were not rushed; there are many distractions and my normal cross check procedures were not in place.
On initial climb I quizzed the Controller as to our first point on the SID and realized we were not flying what we were cleared. He then told us to climb to 6;000 then direct ZZZZZ. We did as cleared. He then questioned us as to which SID we had been cleared and I told him we believed it was the RNAV and apologized for the confusion. The rest of the departure was uneventful.You don't get a clearance until you request taxi at which point you're told to contact Tower. Tower gives you taxi and ATC clearance. Would have been nice to get clearance at the gate. Controller had a thick accent and we made the assumption we understood which departure we'd been cleared but were in fact mistaken.Double check your clearance before you depart even if you think you have it correct. I had a suspicion; but didn't quiz anyone till we were airborne.
Air carrier flight crew reported not flying the correct departure procedure and not realizing it until after contacting ATC.