More than that, free markets guarantee nothing at all. But the historical record is that free markets have lifted far more people out of poverty than anything else.
The most recent example is China turning to free markets, and the resulting vast improvement in their economy.
The US taxpayers who invested trillions (largely in the guise of military expenses) in inventing the tech [1] didn't get to decide freely how the business to be conducted or how the profits to be shared. The Chinese workers (or similar ones elsewhere) didn't get to move freely to places for work with competitive wages.
The rich had the freedom to take the publicly funded tech, to exploit the confined sweatshops, all the while without even paying regular taxes that the ordinary Joe has no way to avoid [2].
[1] https://www.ineteconomics.org/perspectives/blog/what-the-ste... [2] https://www.washingtonpost.com/news/business/wp/2016/03/04/w...
China hasn't turned to anything like textbook Anglosphere free markets. Yeah they loosened up and turned away from classical central planning, but state-owned firms still control 30% of assets and their government does quite a to set economic policy and direction. They didn't privatize everything and let the free market run amok.
[1] http://blogs.worldbank.org/eastasiapacific/state-owned-enter...: With all these evidences in hand, we can now answer the question raised before: How big are Chinese SOEs? Even though their share in the economy continued to decline in the past decade, SOEs still make up a substantial part of the national economy – roughly controlling 30 percent of the total secondary and tertiary assets, or over 50 percent of total industrial assets.
https://scholars-stage.blogspot.com/2014/08/passages-i-highl...
> Westerners often describe China's explosive economic growth as a product of its export sector. This sector, however, is not "in the system": “The private export oriented sector suffered massive losses in jobs, earnings, and the closure of small companies in 2008 and 2009. But China’s banks were not exposed in any material way to this sector. It is simple fact that China’s financial system and its stock, bond, and loan markets cater only to the state sector, of which the “National Champions” represent the reddest of the Red. These corporations, the heart of China’s state owned economy, are “inside the system.” The private economy, no matter how vibrant is “outside the system,” and in fact serves the will of the system.” (p. x)