A319 flight crew reported engine oil pressure fluctuations that resulted in an inflight shutdown. Flight crew returned to departure airport and landed safely.

Narrative

Ram Air Turbine (RAT) pack; rwy XXR. Shortly after plane's cleanup; captain showed and advisory on the upper ECAM display. We checked the lower ECAM display (engine page) and noticed amber xx indication on engine 1 oil qty. then I noticed the oil pressure for Engine (ENG)2 was 52 while 24 psi for eng1 and called captains attention. We saw it dropping to 22 and oscillating; then 20; and we agreed on preparing for what was coming. We called the Lead Flight Attendant (LFA) to let her know that we were having an issue and that might end up in an engine shut down; so they should stay seated and wait for further instructions. Then we got an ECAM warning; Continuous Repetitive Chime (CRC) and ECAM Eng1 low oil pressure. We followed the ECAM instructions to shut down the engine; captain [advised ATC] while I was dealing with the ECAM actions; when a second ECAM came up; this time Auto Thrust (A/THR) thrust lever limited (thr lever move) coming on and off repeatedly; with its chime; caution light and coming on and off on the display. Called captains attention again for the operation of the thrust levers. We decided to 'emergency cancel' that ECAM to deal with the first ECAM (and because different levers movements weren't working). It kept coming on and off. Finally; setting eng2 thr level to Max Continuous Thrust (MCT) worked and we could continue with the eng shutdown; but there were no more ECAM actions on the display. Captain continued controlling the aircraft and navigating back to ZZZ handling the comms (since we hadn't declared 'ECAM actions completed' yet). Since we lost all directives from the Engine Warning Display (EWD); we tried the best we could to 'replicate' the actions studied before and decided to start the APU and review the system pages by manually calling the pages. ATC kept calling with requests and instructions. At this point we were already really stressed because of the situation itself and the environment (early on the departure and really close to the airport to return); so we decided to calm down and evaluate what we had and what we didn't do. We noticed that we were trying to do everything real fast and efficiently because we were already descending to land on rwy XYL; but we lost the 'proper order'; so we started challenging each other trying to cover everything on the procedure; flying the aircraft; navigating and comms. On this proceeding; we noticed we didn't call 'engine secure'; assessed the situation and decided that because the engine didn't fail but we shut down the engine; and we were already too low and on an already safe condition; ready to land; that explanation would suffice. So we continued whit the mutual challenge. Then we covered the 'communicate' part of the golden rules by calling the flight LFA to give a briefing and estimated time to land; called ops to notify our condition; configure the aircraft; re assess the situation and other considerations like the use of thrust levers; possible info in the manual; straight in on engine inoperative approach checklist; etc.Landed safely and within parameters on rwy XYL; vacated the rwy via Taxiway 1 and waited for the trucks to check the engine to continue taxiing to gate XX There might be inaccuracy (and some information that I can add on further efforts to remember if needed) on the order of some procedures but what I am trying to explain is we knew we were out of order; so we tried our best to keep up and meet all requirements; 'checking all the boxes'; on a very stressful situation because of the altitude; surrounding terrain; night time; weight; departure/arrival/landing; ATC environment; etc; and very important; the startle derived from this A/thr ECAM coming on and off that interrupted a well known and practiced scheme. I think that CRM; error management; combined experience and the support of every gear of the machinery helped us to land safely.