Here's an old-school socialist vision for this (say, something along the lines of what Noam Chomsky would advocate):

- society (through local community funds etc) would ensure that everyone, regardless of anything else, has access to basic livelihood (food, shelter, clothes, transport, healthcare)

- society would ensure that everyone has access to the same educational institutions, including required resources (manuals, computer access etc.)

- people would strive to evaluate others based on actual aptitude, rather than class markers (e.g. someone speaking with a heavy "uneducated" accent or wearing low quality clothes wouldn't be looked down upon being evaluated for a professorship or top management position)

- inheritance would be heavily taxed; this would be set up in such a way that people would have a right to the human elements of inheritance - e.g. the home where they grew up, their parents' memories etc. - but huge transfers of wealth, such as inheriting your parents' Amazon stock would not be profitable.

Better off parents will still be able to give a better life and resources to their children, but the impact of that care on the ultimate outcomes will be much less. A "perfectly meritocratic" system would likely be horribly dystopic, such as entirely separating children from parents at birth, Brave New World style.