My characters often have unusual traits or skills, and my solution to this dilemma is two-fold: First, they are born with their skill, along with some deficits. I never grant a skill without a penalty to go with it; in personality, thinking, etc. I also shy away from "best in the world" skills, I may make my character a naturally skilled pilot, but not magically good, and I am careful to have them admire the skills of other pilots they think may beat them.
Often their deficit is just being a non-genius and facing an opponent that is a a much sharper thinker and strategist. The best fighter in the world can be tricked and misled into a trap without ever getting to strike at their enemy.
Second, I give them a problem that they can solve with their skill, but they aren't so sure they can. In fact my main characters often knowingly choose what they consider an enormous risk to achieve their goals, driven by love of those they are choosing to protect. I don't want my readers believing they have a lock on it. So if the MC is a skilled soldier, they face odds they find overwhelming and frightening, and go to war believing they will die in the effort, and of course I give them much to lose by doing so.
As for events occurring in the story, a similar strategy applies: Sure, you were wandering through the woods and found a dead magician, picked up his wand from his dead hand and it frikkin' works for you. And yes, this is going to solve the MC's problem. But it comes with negatives (just like the born skill comes with born deficits). And it isn't all-powerful, you can't just wave the wand and big problems disappear. Or you truly don't know how to use it, so you are incompetent. But readers can accept that the MC they have been following, opening on the MC's normal world, is the chosen one; and finding this wand is what makes them the chosen one. Reader's can accept the MC is the chosen one and whatever "random" incident happened to them is the reason why. We are quickly introduced to Frodo, to Luke Skywalker, to Harry Potter, and just that fact makes them special and it isn't surprising to us they are born special or lucky.
At the beginning of stories, the author has enormous license to introduce magic, telepathy and mental powers, teleportation, consummate abilities, FTL travel, other sentient animals, aliens or machines, and on and on. Just look at X-Men!
The reader is open to anything in the first pages. So introduce your random event very early, in the first 10% of the story, and it can be accepted without a blink. Then the only reason your story will fail is, not because of that, but because things were too easy for the MC after that, there wasn't enough conflict, there wasn't enough wondering how things would turn out, and the story fell into "wish fulfillment" without any significant struggle for the MC.