Can a large passenger aircraft recover from a stall?
The main thing that is required for a stall recovery is just the ability to drop the nose to decrease angle-of-attack and regain airspeed (and, of course, adding power helps, too.) Except in the case of deep stall, there is still sufficient air flowing over the horizontal stabilizers (and, thus, the elevators) in an airliner to push the nose down during a stall. Furthermore, most airplanes (including nearly all, if not all, airliners) are designed with a center of gravity forward of the center of lift. In normal flight, the air flow over the horizontal stabilizers actually pushes the back of the plane down, which holds up the nose. During a stall, this airflow is reduced (still present, but to a lesser degree,) which will cause the nose to tend to drop by default during a stall condition, even if the pilot (or autopilot) gives no additional control inputs at all. As such, normal (e.g. not fighters or aerobatic planes) will recover from a stall on their own with no additional control inputs, given enough altitude.

As already mentioned, some altitude is also usually required for successful stall recovery. This is because the recovery procedures involve dropping the nose which will briefly result in some descent. The lack of sufficient altitude to recover was the main problem in Asiana 214, which crashed just short of the runway in San Francisco. The aircraft was already too low and too slow to recover before the pilots acted. If I remember correctly, they started attempting a go-around only about 7 seconds before the aircraft impacted the seawall. At that point, there was nothing they could do. A small, piston-engine aircraft probably still could have recovered from that situation because piston engines spin up much, much faster than jet engines and could provide the power needed to recover much faster. Pushing the nose down alone would still technically have recovered the plane from the stall condition in this case, but that wouldn't have been very helpful, since it would have meant a nose-first impact into either San Francisco Bay or the seawall, which would obviously have been a much worse outcome.

Another problem that can happen (though is very, very unlikely on an actual airline flight, but much more likely on cargo flights in airliners) is for the cargo to shift to the point that the center of gravity is too far from where it's designed to be for stall recovery to be possible. This is what happened on National Airlines Flight 102, a 747 cargo flight departing from Bagram Air Force Base in Afghanistan. Very shortly after takeoff, the cargo shifted to the back of the aircraft, preventing the pilots from being able to lower the nose enough to keep the plane from stalling. It stalled and crashed before ever leaving the property of the airfield.

In general, pitch stability (more precisely known as longitudinal static stability) is what makes an aircraft capable of stall recovery, not maneuverability. While it may seem counter-intuitive to those not familiar with aerodynamics, it's likely actually easier to recover from a stall in an airliner than it is in a fighter (and almost certainly easier to recover in, say, a Piper or Cessna than a jet fighter.) This is because more maneuverable aircraft (such as fighters and aerobatics aircraft) are usually less stable than less maneuverable aircraft like airliners and normal GA aircraft.

The answers to this question give a thorough explanation of stall recovery which I would recommend reading. Its answers apply to how stall recovery is performed in any normal airplane, not just airliners. That question isn't specifically about whether airliners can recover from a stall, though, which is why I didn't mark this one as a duplicate.