Just because white families are on average financially better off than non-whites does not mean that they are somehow afforded additional societal privileges.
In order for ‘white privilege’ to be contributing to the wealth gap, there must be some form of government policy that gives white people a financial boost, while holding other races back financially. Otherwise, the wealth gap cannot be attributed to white privilege, but another societal factor or current.
This policy does not exist. Therefore, white privilege does not exist.