First of all, I completely disagree with the assertion that the USSR was a neoliberal social welfare state. The USSR was not a liberal state at all, it was a strict totalitarian state where people had neither economical nor political freedom, even during its most liberal times (so-called "ottepel" (thaw), dated approximately 1958 - 1965), and all basic human rights were flagrantly violated. A person could have been sentenced to death for criticism of the government, even in private conversations, or for exchanging foreign currencies.
It's also difficult to admit that there was some kind of social welfare, no matter the meaning implied. With extremely low efficiency of the economy, the government always sought to build up military power at the expense of consumer sectors of the economy, since the cost of maintaining the army and its infrastructure was exorbitantly high. People's standard of living was several times, even tens of times, lower than that in developed countries. During almost all of the history of the USSR, there was a shortage of goods, even everyday staples, like bread, meat, butter, and sugar, were impossible to buy freely, and were distributed by rationing. In early 1930 between 2 to 4 million people died of starvation, another million died of starvation in 1947-1948. A worker could hardly afford to buy a car until the 1970s (the price of a car was comparable to a worker's salary for 5 years, while people had to spend almost all of said income to buy food and clothes), and even then one had to wait 5 to 10 years before they could actually get the ordered car.
After the socialist revolution, under Lenin, all the industry was forcibly nationalized (confiscated from private owners and transferred to the government). After introducing NEP, ownership of private business was legalized and some small enterprises were re-privatized, and other private entities were started from scratch. Large industrial enterprises were not privatized, but the conditions of their operation were liberalized and in their activities, they partly used the principles of a market economy. Most of the private enterprises were small local businesses, like shops, restaurants, bakeries etc. In 1923, 92% of industrial product was produced by state enterprises,while private business produced 5% and the rest 3% was contributed by cooperatives. (source, you may use Google Translate to read it) By the end of the New Economic Policy the share of the private business had grown, but not significantly, different sources say about 7% to 10%.
At the end of the 1920s, the NEP was completely stopped, and all private businesses were nationalized once again. Since 1931 owning any form of private enterprise was considered a serious crime. See also Law_of_Spikelets. This situation lasted till 1988, when the "law of cooperation", which actually legalized private enterprise, was issued.