You can get a highly paid desirable job with access, so think Kate Moss's daughter now a model herself.
So access to opportunities is one factor.
Confidence is another, this can come from having a family cushion in case you fall but the confidence to take chances, some work some fail.
As for high achieving children from average families, education. If you want to be an IT guru, or maths whizz working out probabilities for insurance companies (this pays quite high) you have to be able to actually do some stuff. This is a route to achievement.
University opens many doors.
You don't need cello lessons or trips to the Caribbean if you can embrace all the opportunities state school and your local area can give you.
Instill in your children a work ethic, resilience, emotional and social intelligence, that the world doesn't owe them a living and that's a good base to climb from.
Look at footballers, very few of their children become footballers, because being Daddy's son isn't enough you actually have to be one of the best footballers at that time.
There's no secrets. There is no single path to high achievement. Partly because it means different things to different people.