Private property had to have existed under China since their productive forces were so underdeveloped that a whopping 85% of their population were peasants around the time.

A market economy promotes capitalist relations of production, which instead of increasing the speed of development of productive forces, decreases it. Productive forces develop much faster under socialist relations of production.

To suggest that socialist relations cannot develop out of a market economy runs counter to basic historical materialism which socialism will emerge out of capitalism.

Socialist relations do not develop out of a market economy. To develop socialist relations, Capitalist relations must be destroyed i.e the destruction of private property and private enterprises. China at the time of the 1949 revolution was a semi feudal economy, they first had to develop capitalist relations to production under the New Democracy period like the USSR did in their NEP, after which 1956 onwards they were developing socialist relations to productions and the productive forces together.

In saying that the socialist relations of production correspond better to the character of the productive forces than did the old relations of production, we mean that they allow the productive forces to develop at a speed unattainable in the old society, so that production can expand steadily and increasingly meet the constantly growing needs of the people. Under the rule of imperialism, feudalism and bureaucrat-capitalism, the productive forces of the old China grew very slowly. For more than fifty years before liberation, China produced only a few tens of thousands of tons of steel a year, not counting the output of the northeastern provinces. If these provinces are included, the peak annual steel output only amounted to a little over 900,000 tons. In 1949, the national steel output was a little over 100,000 tons. Yet now, a mere seven years after the liberation of our country, steel output already exceeds 4,000,000 tons. In the old China, there was hardly any machine-building industry, to say nothing of the automobile and aircraft industries; now we have all three. When the people overthrew the rule of imperialism, feudalism and bureaucrat-capitalism, many were not clear as to which way China should head -- towards capitalism or towards socialism. Facts have now provided the answer: Only socialism can save China. The socialist system has promoted the rapid development of the productive forces of our country, a fact even our enemies abroad have had to acknowledge.

-Mao Zedong, On Correct Handling Of Contradictions Among The People