B737-800 First Officer reported decreasing hydraulic system A pressure during initial climb. Flight crew returned to departure airport; landed; and taxied to gate.

Narrative

Engine start at the gate due to no APU; took us two air carts to start the engine; we start the second on the taxi out and hold short of the runway to do the after start checklist; where I note to the Captain that the controls are stiff; he checks them as well and notes the same; but within tolerances.After takeoff and gear up; we get a master caution light with HYD recall light; where I look up and notice that both HYD A LOW PRESSURE lights have flashed on for several seconds; and quickly switch the SYS page where we watch the HYD A system rapidly lose pressure down to approximately 70%; and then slowly bleed off down to the lowest of around 67%. Captain hands me the controls and I [request priority handling]; we get vectored around while he takes care of the QRH and I set up the airplane for the return to the field. While he takes care of the Flight Attendants (FAs); QRH and associated items I inform ATC of all the necessary info. We begin the arrival and land on the runway and come to a stop while Airport Rescue and Firefighting (ARFF) checks on the plane. They note they don't see anything wrong; and we get the gear pins installed and taxi under our own power to the gate. We chat with Maintenance a bit after engine shut down and give them our notes; debrief with the FAs and deplane.The training department did an excellent job of instilling exactly what we needed to do during this exact scenario; I am glad it played out as it did because both of us knew exactly what part we needed to play.I am not sure that we could have done anything outside of what we had done to prevent this from occurring.