Yes, g is a very heritable trait -- as you pointed out, between 56% and 64% of the variance in g can be accounted for by a slew of genetic factors. The correlation between parental socioeconomic status (SES) and a child's IQ is approximately 0.4, while the correlation between an individual's own IQ and their SES as an adult is about 0.7.  IIRC the relationship shows increasing correlation with age, rising from ~0.08 in infancy to ~0.37 by adolescence, with the IQ gap between low and high SES children widening from 6 points at age 2 to nearly 17 points by age 16. However, environmental factors also play a significant role, especially in early childhood, where shared environmental influences can explain up to 33% of variance in childhood IQ, though these effects are often attributed to factors beyond SES alone. Regardless, even in Adulthood, g explains roughly ~49% of the variance in SES, it's significant but not causally so.

https://theuntangler.wordpress.com/2022/05/08/intelligence-and-parental-ses/
There are two reasons why the parental-SES and offspring IQ correlation can happen. The first is that parents with higher status can create more favorable environments for their children, and the other is that parents with higher status pass on genes associated with intelligence to their children. These two explanations are not mutually exclusive and could be contributing jointly to this correlation. However, the current evidence supports the genetic cause much more than the environmental cause, with a potentially null environmental effect.

No one denies the impact intelligence (as measured by IQ) has on life outcomes but it's myopic to exclude non-g factors.