Yep! And the research confirms what you've said.

"Advantages beget advantages. Those who are born in the upperclass echelons are likely to remain in the upper class (Wilkinson & Pickett, 2009). The majority of individuals who work at elite and prestigious firms tend to come from elite educational institutions (Rivera, 2016). And high-earning entrepreneurs disproportionately originate from highly educated and well-to-do families (Levine & Rubinstein, 2013). These are some examples of how advantage tends to be self-perpetuating, belying the American ideal of social mobility (e.g., Hochschild, 1996). (2)

In terms of access, we find a distinction between traditional professions, such as law, medicine, and finance, which are dominated by the children of higher managers and professionals, and more technical occupations, such as engineering and IT, that recruit more widely. Moreover, even when people who are from working-class backgrounds are successful in entering high-status occupations, they earn 17 percent less, on average, than individuals from privileged backgrounds. (3)"

https://medium.com/inside-of-elle-beau/incompetent-rich-people-often-get-ahead-ffa51b44bf69