Excuse one’s ignorance, I know there was famine, didn’t that lead to fears of over population and one child policy?
Not at that point, no. The One-Child Policy was a product of extrapolations in the mid-1970s which showed that the population would outstrip the country's ability to feed it, let alone improve the standard of living. In the 1950s, Mao was still banking on surviving a nuclear war with the US through having more people than they could nuke.
The GLF was essential an attempt to force an
industrial revolution by creating a surplus of urban labour and improving agricultural efficiency to feed them. The trouble was, nobody realised the extent to which the rural poor wanted to **** off as far away from the countryside as possible and earn a living indoors, so as soon as the government relaxed the household registration (hukou) rules the young and healthy buggered off at Warp Factor 9.
This left the very old, the very young, the very badly educated and the very crippled as the largest demographics and opened the doors to some utter looney-tunes ideas about how to make up the productivity gap. Add in a brutally coercive political system which demanded adequate food supplies for the cities and the rural folks were pretty much at the mercy of whether their local party heads had a conscience or not. Yang Jisheng's
Tombstone is one of the finest works on the subject, although not one to read if you have any illusions about your fellow man.
It's also one of the reasons why the government has been so reluctant to carry out wholesale reform of the
hukou system to this day. They learned what could happen.