Absolutely. There are certain things that will make it easier--like having very good proprioception/kinesthesia, or perfect vision--but with enough focused time and practice, almost anyone can become a highly proficient shooter. Some people will definitely have an easier time than others, and some abilities in other areas will help more than others. And yes, you absolutely need to practice or else you'll start losing your ability.

But.

As far as needing to be introduced to shooting early, absolutely not. There are a number of people that have moved to the US in their middle age from other countries (Korea, in particular) with no experience with firearms, taken up shooting, and have become USPSA masters and grand masters, because they understand how to practice.

Depending on what you want to learn, my first suggestion would be to look up NRA classes. Yes, yes, I know, but trust me, the NRA classes are very good for foundational work. You want to start with safety and get very, very familiar with that before moving on, because carelessness with a firearm can kill. From there, you can do something like Project Appleseed to get proficient with rifle marksmanship, or you can take classes with Ben Stoeger and Joel Park for pistol.

Hunting specifically is going to require far, far more than shooting ability; you're going to need naturalist skills, like being able to see trail sign, land navigation, getting a feel for movement without spooking animals, and so on. For hunting, most of your time will be spent in observation and waiting, with only a single shot at the end of it all. Spending a lot of time outdoors, in the woods or fields, paying attention to animal behavior is your 'practice' for hunting.

Aside from all of this, something to consider is that the average shooter is... Pretty bad. Most people that own firearms don't put in any significant amount of time training. The police are no exception; most cops are not terribly proficient with their weapon, because they only have to qualify annually, and qualification is slow fire at a target 10y away, not a practical shooting course.