In 1913 meat production per head of population on that territory had been 58.1 per cent of the US level. As late as 1958 it was only 48.0 per cent. Milk production per head of population had been 72.8 per cent of the US level in 1913. In 1950 it was only 51.6 per cent of the contemporary US level, and in 1953, 52.1 per cent.
With Stalins death in 1953, the new Khrushchev government initiated a huge shift to consumer focused investment(largely agriculture) rather then the Stalinist industrial focused investment. There has been a saying since the 60's that Stalinist production was focused on building machine tools to produce machine tools to produce machine tools ad irifinitum. In the 50's state payments for crops rose hugely, both for state run cooperative farms and for personal plots. The official index of farm procurement prices rose almost three-fold between 1952 and 1958. This was at a time when retail prices were officially unchanged, leading to huge increases in consumption.
Compounded onto this was the large scale extensive growth in the 'virgin land' scheme, where huge amounts of soviet investment were put into fertilizing and preparing the Kazakhstan region for cultivation. These types of projects were common throughout the soviet era, as for planned economies an extensive growth in the inputs of production is much easier to accomplish then the intensive growth with existing inputs as we see in modern economies.
The early surge in farm production encouraged him to talk in 1957 of overtaking American per capita meat production by 1975, something to which the Soviet Union never came close. Reliance on the unstable grain harvest from the Virgin Lands produced acute difficulties when the harvest failed both there and in traditional grain-growing regions in 1963.
Talk of overtaking the US both in terms of meat production and in terms of the general economy now looks silly. At the time, it was not obviously so. At a continuation of the growth rates from the 50's, the soviet economy was expected to overtake the american economy in the 70's. Recent past growth in farm output had been impressive (In a 5 year period meat consumption went from 27.5 kg per person per year to 34.8, milk from 144.8 to 200.9, grain from 247.9 to 297.6). As with space travel, so, at the other end of the technology spectrum, with farming: this was a time when the Soviet economy really did seem capable of great achievements.
By the early 70's, soviet agricultural consumption had generally been increasing compared to the U.S, at the cost of other consumer goods and electronics in which the gap had been ever widening. This table summarizes consumption differences between major goods in the year 1973, however this of course lends itself favorably to the limited variety of goods that a planned economy provides.
After this point, the soviet economy and agricultural industry was placed into a period of general stagnation that saw it shrink comparably towards the US until its dissolution.
Source: Hanson, the rise and fall of the soviet economy, 2003
Apologies if this does not constitute a full answer, or meet the subreddit's standards, but it seems like OP wants a specific source, and might be referring to something like this CIA document. Of course it's difficult to know specifically what source OP's aforementioned book used, as the CIA produced a fair number of resources on the Soviet diet.