The commission's Time for Change report into social mobility policy since 1997 concludes successive governments have made "too little" progress to tackle gaps between rich and poor across education, training and employment.
Among improvements being called for is a substantial investment in early years education, including doubling the annual £300 per child early years pupil premium for disadvantaged children.
The commission says this would enable childcare providers to offer extra support.
"From 2015, government offered extra funding for teachers of disadvantaged pupils via the early years pupil premium. While helpful, impact was limited by low levels of funding," states the report.
Government is also being urged to set a national target of halving the attainment gap between disadvantaged five-year-olds and their peers as well as ensuring all children are school ready within the next 10 years.
At current rates of progress the commission estimates it will take 15 years before all children are school-ready and 40 years before the attainment gap among five-year-olds is closed.
The commission also wants to see more funding for parenting programmes, early years classes delivered online and a better pooling of Department of Health and Department for Education budgets to support disadvantaged young children.
"The proposal to increase the early years pupil premium would be a welcome step, but unless this is part of a larger government effort to do more to support children from more disadvantaged backgrounds, there's only so much this can achieve," said Neil Leitch, chief executive of the Pre-school Learning Alliance.
"For far too long, childcare has been used as a political football, with all parties appearing to prioritise a short-term desire to win votes over a long-term ambition to improve children's life chances. As a result, over recent years we've seen ill-thought-out policy after ill-thought-out policy, most of which are not only significantly underfunded, but don't actually help those families that need the most support."
The commission's report also found that spending on education has fallen since 2010 in real terms, two thirds of children on free school meals do not get good GCSEs and employment prospects for young people from low-income families are poor.
The commission estimates it will take 120 years at the current rate of progress for disadvantaged young people to be as likely as their better-off peers to achieve A-level or equivalent qualifications.
"For two decades, successive governments have made the pursuit of higher levels of social mobility one of the holy grails of public policy. While there has been some progress, it has not gone far enough towards translating welcome political sentiments into positive social outcomes," said commission chair Alan Milburn.
A national target is being called for to close the GCSE attainment gap between poor children and their peers within a decade.
Another recommendation is an overhaul of apprenticeships to focus more on young people. The commission found that over the last 20 years the number of young people taking up places has barely increased, with government funding instead increasing participation for the over-25s.
Save the Children chief executive Kevin Watkins said the failure by governments to support disadvantaged children is "nothing short of a scandal".
"We all know that unless we get education right in the early years of a child's life, so many of them - especially the poorest - will struggle right through to their GCSEs and beyond; into the world of work and even in their relationships," he added.