There's no good reason to believe that Zuckerberg is lucky at all. Saying he was in the right place at the right time has this tacit assumption that if he were somewhere else at the wrong time he would have tried the same thing and fell flat on his face.
It seems because Facebook is an outlier, people feel safe talking about the luck factor, but that's meaningless because we all exist with individual circumstances, and by that measure everything every one of us does is based on luck. Instead, I prefer to ascribe luck to things that the individual actually had no control over, such as winning the lottery.
Being the right place and right time is a huge part of it. He was the right age, in the right environment, when the right technology reached the right tipping point and critical mass.
I'm not disparaging Zuckerberg's ability or hard work. However many with greater ability and who have worked harder have failed because of circumstances beyond their control.
Yes, there is, in the literally uncountable possible paths that the decisions of every other person on the planet (not to mention the state of the planet itself) create, there probably does exist a path to success, if not all, at least most people. Some of those paths involve crime, deceit, coercion and such but that is irrelevant.
"Luck" is you making the right choices (naturally based on your genes, psychology and the decisions that have led you to your current self), others making choices that facilitate it and the planet not blowing up in this process.