The short answer is: yes, this is not an unrealistic goal and you can almost certainly reach it. Like most skill sets, how long it takes to learn it will depend on how vigorously you pursue your goal. Really single-minded devotion to preparation could see you ready by next autumn, but most of us have too many responsibilities to be single-minded, so if you've never really done any camping or hiking before, give yourself a year at least to study up and start practicing your skills.

Most of the skills required for backpacking are simple to learn, but not all of them. The easy skills are things like how to pitch your tent, tarp, or hammock, or how to select your food so you neither go hungry nor walk back out to your vehicle carrying 5 lbs of uneaten and unnecessary food, and how to pack your pack and adjust the hip belt and straps for maximum comfort. These simple skills, once you've practiced them a bit and are comfortable with them, can be applied with minor variations to most of the hikes you'll do in the future.

Read up as much as you can before you spend any money! There are many good books, websites and forums out there, but read more than one, until you find an approach that makes sense to you. Carefully select your gear and clothes, then take a few short 'shakedown' overnight trips. That ought to cover most of the easy-skill learning curve. Oh, and the best way to get in condition for carrying a pack is... carrying a pack.

The skills that take longest are more connected to developing a keen sense of the place where you hike, such as understanding what clothes will keep you comfortable and safe in all conditions you are likely to meet, recognizing a change in weather several hours before it arrives, and knowing the topography of your surroundings well enough to predict a water source or a good campsite. The less well you understand the place you hike, the more safety factors you need to build into your plans to compensate for that lack of knowledge.

If you choose a national park for your adventure that is far from home and unlike anywhere you've ever been before, it will present a greater challenge and be harder to prepare for than if you seek out a place nearer home. But don't confine yourself to national parks. They can be crowded and have many restrictions on where and how you can camp in them. National forests and wilderness areas may provide a better opportunity for the kind of trip you envision.

By the way, I live in the Pacific NW. The shadiest NP near me would be Olympic National Park. It's a rain forest!

Others here will add many more valuable bits that I've forgotten to mention. Taken together, our members represent a huge amount of practical experience and hard-won wisdom. Good luck!