I found the fastest way to be able to get a shotgun "aimed" was practice bringing it up from a 2 handed carry to my shoulder in low light - with a drop of White Out on the bead to highlight it. You need to learn where the gun fits you "naturally" and where the rear sight line is in your natural "ready" position. Form there, you can almost ignore it and just focus on the bead and putting it on the target.
Soemthing I was told years ago as I was learning that helped me:
Even with your eyes closed, you will always know where your hands are in spatial refence to your head/eyes. You can make a gun shape with your hand, eyes closed, and point it anywhere in the room. Look at your raised thumbnail (the pretend hammer) "in your mind", and then open your eyes. You'll be looking directly at your thumbnail. Holding a shotgun is pretty much the same ... visualize your thumb reaching for the hammer of an old double barrel and you'll be instantly looking at the rear sight line of your shotgun.
After that, it's ensuring you have a gun that fits you comfortably and sits farily true and level when it's in a shooting position. You should be able to raise and point it straight out in fornt of you with your eyes closed, and on opening your eyes, the sights shoudl be close to lined and level. I found I was prone to having the bead naturally sitting about an inch above my "natural" shooting position - soem time doing drills of raising, aiming, then opening my eyes (with an unloaded gun of course) - and paying attention to body position throughout - soon cured me of that and I created the muscle memory that enabled quicker, more accurate sightings, which comes in very handy when pushing brush for bunnies, partridge, etc.. and paddling streams and rivers for ducks - carrying your shotgun on your shoulder looking down the bead all day "commando style" while looking for game is a VERY tiring process. The time spent learning to "draw" it from a normal carry position is well worth it.
After all of that .... practice, practice & more practice is the true key

It's all about creating the muscle memory of a good ready position for each gun you carry.