It's virtually impossible on a reasonably modern firearm that is in good shape. When I bought a new pistol a couple of years ago (it was a new design, released only a few months ago) one of the first things I did was test that it wouldn't discharge accidentally. I emptied the pistol, cocked it, and while holding it in one hand whacked it repeatedly with a short section of a 2x4 from all directions to simulate dropping it. It stayed cocked.
Obviously, any poorly-maintained and/or worn out firearm can have mechanical failures, even a modern one.
Having said that, older designs (including freshly-made older designs) can be discharged without touching the trigger. The original revolver designs were "single action" handguns. The trigger only has a single function: release the cocked hammer. The hammer had to be cocked by the shooter, typically with the thumb. This is the kind of gun typically seen in cowboy movies.
Now, because the shooter had to cock the gun manually, it's possible for the thumb to slip, letting the hammer snap forward before the trigger mechanism has a chance to catch the hammer and hold it. The gun makers put in "half cock" and in some cases "quarter cock" notches in the mechanism to help prevent this. But if Baldwin was getting a feel for the gun and let the hammer drop before it got to the half-cock notch, then the gun might go off. Of, if the gun was poorly made or worn out, the half-cock notches may not have worked as intended.
Since a full cock of the hammer also rotates the cylinder, it's possible that if he was doing some repeated partial-cocking and letting the hammer drop each time, he was actually tapping the same cartridge in the same spot over and over again until it went off.
It's also possible that Baldwin had fully-cocked the revolver. Well, if you do that the only way to release the hammer without firing the gun is to hold the hammer back with your thumb while you squeeze the trigger, then gently lower the hammer down to the rest position. If he slipped on that operation, the gun also might have gone off.
I will note that with modern revolver designs it is impossible for the hammer to touch the firing pin unless the trigger is pulled back. The firing pin in mounted in the frame of the revolver instead of protruding from the hammer, and it is shrouded from the hammer. A steel bar called a "transfer bar" is controlled only by the trigger. When the trigger is pulled back far enough (just before the trigger releases the hammer) the transfer bar fills in the gap between the hammer and the frame-mounted firing pin so the energy from the hammer gets to the firing pin. If the trigger isn't pulled back far enough, the dropped hammer will not be able to reach the firing pin because the transfer bar isn't in position.
There are other factors with the accident that may involve the ammunition as well. There are three kinds of ammunition possible: dummy or inert rounds, blank rounds, and live rounds.
Dummy rounds look real but have no primers or gunpowder. Usually there's a hole drilled into the side of the case to show the lack of gun powder. They are used for close up camera shots.
Blank rounds have a charge of powder but no bullet. Typically the case is crimped closed. These rounds make the "bang", but are not lethal unless the press the muzzle of the gun up against somebody. I believe this happened once; some stunt guy killed himself while fooling around with a blank gun. Held it up to his head and pulled the trigger, and the shock wave killed him.
Live rounds are the real deal: bullets and powder.
Supposedly the crew was using the revolver to shoot live rounds recreationally when off the clock. If dummy rounds and live rounds got mixed up, that could be what caused the death and injury. Baldwin should have known what was in the gun, but it's also possible that he was instructed poorly or incorrectly. He's an actor, not a gun user. I don't expect him to really know about guns any more than I expect Tom Cruise to really know how to fly an F-14.
But Baldwin is not just an actor on the set; he's also a producer of the movie. If another actor had discharged the gun and killed one and injured another, he'd still be on the hook for the shitty way the production was being run and the general incompetence of the set armorer.
Regardless, the gun is in evidence and can be analyzed to figure out if it working properly, and to figure out exactly all the ways that gun can discharge a cartridge.
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