You can take steps to reduce it, but we don’t (nor should we) have the will to eliminate it.
My kids will have advantages over the median kid in America and my wife and I work hard to ensure that. I don’t have to be specifically seeking to give them a relative advantage, but everything parents do to ensure an absolute improvement in their life outcome represents a relative advantage as well.
We ensure medical care, nutritional food, calm, regular, and loving interactions with adults, social and physical learning through play, clearly prioritize academic achievement, take care to discipline them appropriately, allow them to struggle-then-succeed at many things, expose them to science, cooking, math, computers, electronics, live in a house full of books and Kindles, have a family pet, take trips to local museums and farther off places, expose them to music, a second language, various sports, ensure they feel safe/secure/loved, that they have a quiet, comfortable place to sleep, etc. We’re fortunate to be able to do these things, but it also takes some sacrifice to do them.
If you want to remove those influences entirely, I can’t see doing it without having the state raise the children in standardized conditions. And of course, no one would tolerate that.