Got to support what's already been said.
I raised 5 and now have 9 grandkids, so far, all love the outdoors lifestyle.
Youngsters love to be with their Dads. The only thing they love more is their Moms.
What ever they see Mom and Dad do, they want to do. They want to copy and emulate the humans they are bonded to and they want to please you by showing you they can do what you do.
Then they are little (3-6) they naturally love the outdoors and the never ending discovery associated with interaction in the sights, sounds, and smells of mother earth. (If you wait much past 4 or 5 years of age to get started outdoors they find other interests and actually dislike the more "harsh" natural environment.) Fear is a result of encountering something that is foreign and unfamiliar, the older they get the more fears they develop. Generally the only thing a really young child fears is something that hurts them. When they are little they will plow head long into most anything, eat worms, hold snakes, kiss fish, walk thru fires, crawl under a rotten stump, roll in the mud, wade a creek, climb a tree, whatever. They want to see, feel and taste everything in their new and wondrous world. If they are never allowed, with the watchful eye of a cautious but understanding Dad or Mom, to wallow in the arms and legs of the wild outdoors, at a very early age, they will grow up to fear and dislike it. If you wait until they are 8 or 9 years old, for many, it's too late because they have already developed a great many believes of what's satisfying and what's not. By 8 they not going to put a worm in their mouth to feel the texture!
By the time my kids were 4 they were shooting a Red Ryder BB gun and a fiberglass bow and arrow. By the time they were 6 they had fired thousands of BB's at every imaginable target, release a thousand arrows at the same targets. They'd spent entire days, from sun up to sun down being my little hunters in our backyard and in our camps on the mountain. During these early years I watched them like an old bad tempered bear, to protect them and protect what they might bounce a BB or a field tip off.
From the time they were 2, then I was "road hunting" they were in the truck, glue to the windows, they spotted a great many rock and stump deer, I checked every one, "there a deer Dad", they called out, I encourage them to keep it up, never discouraging them when they mistook a sagebrush for a buck. They were there when I pulled the trigger, saw the results, learned to love and respect life and the reality of death and appreciate the hunter/game dance. They learned to love all aspects of man and nature and man's duty to protect and preserve the wild side of the world.
As they grew older 8-10 and demonstrated more responsibility and understanding of the consequences of their actions, I moved them up to pellet guns and let them take a few shots with a .22 rifle, always within arms length, every coaching and restricting if necessary as they learned to use more powerful weapons. We bought them bigger bows and gave them more freedom as appropriate. I allowed them to shoot sparrows, blackbirds, starlings, squirrels and on occasion a few rabbits. I told them not to shoot robins, meadowlarks, and other song birds and when they did I let them know my displeasure and we talked about the difference between nuisance species and desirable species. (Yep, I know all species have value and belong in the eco-system and all life is valuable and we had many, many talks about that too.)
As they grew older (8-12) I took them on off road hunting/fishing trips, over night camps under the stars, away from the roads and down in the canyons, I tried to be careful no to demand too much or let them get too cold but they learned the difference in road hunting with Mom and they younger kids and putting on the packs and heading out for a couple of days. Some times they couldn't take the snow or cold wind and wanted to head for camp early, I usually called it quits early if they'd had enough but as they got tougher we'd stay out longer.
By the time they were 14 they were spending every after school evening in the back yard shooting 200 arrows in a stack of hay bails and bagging to shot clay pigeons with the 20 gauge we'd given them on their twelfth birthday. Saturdays were the same, arrows and pellet guns, off to the surrounding hills on their own, by now I trusted them to take off on there own so long as I knew the general area they were in and when to expect them back. They had already, by 14, learned how to be comfortable in the outdoors.
I took them to Colorado so they could hunt deer at 14, hauled them to New Mexico to hunt elk at 16 (They had the tags, I didn't, I was the camp master, chauffeur and the financier.)
By this time my sons had attended many Wildlife Board Meetings, learned the regulations and the logic behind game management. They were committed to the life style. Dated young ladies from families that had common outdoor experiences,
purchased appropriate vehicles (pickups) and spent their limited dollars on outdoor equipment.
In addition to hunting and fishing they were all involved in school sports, (State Championships) dating, after school jobs, attended their church services, visiting Disneyland, going to boring family reunions, etc. My youngest son worked enough during his sophomore and junior years of high school to save $5000 which he spent to go on a caribou hunt in the North West Territories of Canada before he was a high school senior. He paid his own airfare, his own outfitter, and tipped his own guide without a single dime from his Dad or Mom. I'm not attempting to brag on my kids but I just wanted to make it clear that, besides being immersed in hunting and fishing everyone of them enjoys and participates in all the other "normal" activities that most of our youth enjoy.
There were many, many times when I could have left them at home, it might have been easier, I might have stayed out longer, I might have spent more time with my buddies but I wanted my children to love outdoors and have a lifetime commitment to the way of life that comes from understanding and respecting the real world so I made the investment and in my mind it has paid off. They are now carrying my back pack and looking out for me, I respect them.
So..........to answer the original question, start from the minute they can eat solids, be their mentor, don't leave it to anyone else, give them your time, give them more time, take time, make time, take them BB gun hunting without your .22, take them fishing without your rod, when they're with you, dedicate your time to teach them how things work, how to make it happen safe and make it easy. Make the outdoors comfortable and familiar by frequent opportunity.
I've watched a lot of MMers post pictures of their children engaged in hunting and fishing, i've read stories of their experience with their children and I'd bet you a rib-eye they have raised their children in a very similar way. There's not much of a mystery how to get kids to love hunting but it does take your commitment to the family. Rare cases when children pick it up on their own, good for them if they do, but you can sure improve their odds if "you" do the work.
Hope this doesn't sound like I'm tooting my horn, I feel fortunate that I've had the opportunity and wish you and your children the very best from your outdoor adventures.
DC