How does a several-hundred-pound bear sneak up a veteran hunter/tracker?

Well, it's a movie. So there's that.

You haven't spent much time outdoors have you? The woods make all kinds of little noises. Small critters can make big noises, and sometimes big critters make no noise at all. Plenty of people have been injured by, or at least had a close encounter with, a bear because they surprised it. It's not even remotely unheard of. Moose too, and moose are bigger than bears are.

Atop that, the event happened in life, so why would you find it not believable. Just because he has experience hunting and trapping, doesn't make him superhuman.

A bear with cubs knows that the cubs are vulnerable. Cougars, Wolves, and especially other bears, are threats to them. Stands to reason that a mother bear with young cubs wouldn't advertise her presence.

Well that bear is also a veteran hunter/tracker. Its not just some clumsy creature that stomps through the woods.

I don't think you've analyzed the situation correctly.

The mother bear did not sneak up on Glass. The mother bear and her two cubs were in the woods, just hangin' as bears usually do. The cubs drift off always from mom to play, as kids usually do.

Glass, skillfully and silently, comes upon the cubs. The problem was his approach put him between the mother and the cubs. Its not necessary for the mother to be moving or stomping around. She's just been sunning herself in that spot for the last half hour as she does every day. Or maybe catching a few winks because the cubs keep her up at night. She doesn't even have to hear Glass. She just decides to take a look towards the cubs to see what they're up to. And what she sees she doesn't like.

She didn't sneak up. She was hidden behind something, so he couldn't see her. He knew she'd be around because of the cubs. Then she suddenly came running at him. Despite their size, bears run fast and can outrun a man.

Glass made a schoolboy error here as the bear approached him from the rear. This meant that Glass was left with a bear behind...
(Yes, I know. Sorry about that...)

I think you're looking at it from a 2016 urban mindset. I think it can happen easier than our modern minds would think. Think about traveling through dense woods alone for what I assume is hours. If you have ever walked through the woods alone you would understand how loud yet hypnotic the sounds can be. I mean in a forest that isn't on a trail with 20 other people around you. I grew up in Northern Wisconsin and if you've grown up playing in the woods you will also understand what I'm getting at. I also wouldn't think your mind would stay 100% alert for that amount of time. If you could then kudos to you! I think he was just thinking about all the *beep* that just happened and is as always worried about getting himself and his son out of this alive. Yes, he walks himself right into the worst situation with absolutely no good outcome. As in he is *beep* It's not like making a mistake at work or any other mistake that you could make in your modern life. There is no good outcome. He just needs to survive for his son.

The way I interpreted the scene is that nature is always waiting to destroy you, even if you have a lifetime of experience. It takes a second of having your guard down to have your world destroyed.

You have to take my post with a grain of salt though, cause I absolutely loved this movie.