I think that the answer is a fleeting one, ever changing.
How YOU shoot is a great determining factor, and by that I don't mean how you hit.
A person that is learning truly instinctive style (a name only, we do not have an "instinct" to shoot), it may take a given time.
By using any other aiming technique, that time MAY be cut down, often quite substantially.
As we see at the range, add a compound device, sights front and rear, release, ad nauseum and obviously it takes much less time. Other steps (three under, point on, gap, string walking etc) might help speed the process as well.
Also.. How Far we think we need to shoot is an added factor. Getting good at 5 yards,and at 10 yards is likely going to come quicker than at 50 yards.
Also.. our own personal "X factor", my word of the moment for your ability to do the shoot sequence under the pressure of the hunt: in a tangled web of forest (not on a manicured back yard range); with a target that is not static and just standing there allowing for long time thought and aiming; and with a target that inherently causes some / most / all of us at least some degree of anxiousness.
All of those things change and cause differences in the amount of "time it takes to be good".
Can I suggest a course of action ?
Get good at a range. . say 5 yards, or 10 yards. Then go hunt. You need that hunt practice almost as much as you need the shooting skills practice.
DON'T shoot beyond your known skill. If the deer is 5 yards too far, it gets away this time. There will ALWAYS be deer walking just a bit too far away, no matter your skill. As you increase your ability, increase your hunting range accordingly.
I am a believer that most folks should not wait to hunt until they reach some lofty shooting goal. There are other factors that count too and those are only met and overcome by doing it.
A knowledgeable mentor helps speed the game immensely.
ChuckC