I don’t have figures for their overall national production output during this period, but I can give you some useful information on how many war materiel they fielded or produced.

Stalin was heavily involved in building the USSR into the military-industrial might it became in the 1940s. Before he stabilized his power in the late 1920s, the USSR was a very backward nation militarily, and even up till the 1930s, by which time the USSR was far from weak, this still gave the impression that they were extremely weak, so much that most Europeans in the 1930s considered the French Army as the most powerful in the world. In fact, David Glantz have strongly argued that if Germany had attacked the USSR in 1937 (which was just before the Great Purge) or in 1943 (by which time the reforms that begun in late 1940 would have been completed), Germany would have been defeated outright.

In 1928 the USSR had only 92 tanks and 1,394 aircraft, but by 1935 they 10,180 and 6,672 respectively [Ov]. By June 1941, the USSR fielded 19,533 aircraft and 22,600 tanks [G]. Germany, on the other hand, could only muster 5,639 tanks and assault guns, and only 1960 of these were Panzer IIIs and IVs; the rest were borderline obsolete or straight up useless in combat [Ba].

To put it simply, USSR military production in the 1930s was greater than Germany's. And by 1943, it wasn’t any different. In that year, Germany produced a total of 10,747 tanks and assault guns, while the USSR produced 24,006 tanks and assault guns (or self-propelled guns) [Z&A]. But according to a report published by the U.S. Institute for National Strategic Studies (National Defense University) in 1997, American military production in 1943–1945 was greater than that of Britain, Germany and USSR combined [NDU].

References

[Ba] Pier Battistelli (2008). Panzer Divisions: The Eastern Front 1941-43. (Book). Page: 65.

[G] Martin Kahn. Russia Will Assuredly Be Defeated’: Anglo-American Government Assessments of Soviet War Potential before Operation Barbarossa. (Peer-reviewed journal article). Link: http://www.tandfonline.com/doi/full/10.1080/13518046.2012.676498.

[NDU] Alan Gropman (Editor) (1997). The big 'L' : American logistics in World War II. (Report). Page: 2.

[Ov] Richard Overy (1998). Russia's War: A History of the Soviet Effort. (Book). Page: 55. My comment: I don’t know what sources or analysis that led Overy to those figures, but I take his words on the basis of his proven credibility.

[Z&A] Niklas Zetterling and Anders Frankson (2000). Kursk 1943: A Statistical Analysis. (Book). Page: 8. My comment: Zetterling and Frankson are highly reputed WWII historians with a significant number of peer-reviewed journal articles under their belts.

Hiya!

Your newer understanding that the Soviet Union was, indeed, a massive industrial power is correct. Though I wouldn't claim that it rivaled that of the United States, the USSR's military industry dwarfed that of Nazi Germany's at the onset of World War Two, and this disparity had grown even larger by the German invasion of 1941. It's a common misconception that the Soviets defeated Germany through little more than endless supplies of manpower. The myth of General Winter defeating Germany in 1941 is another. To demonstrate the monumental disparity of Soviet and German military industrial capabilities, I'll compare the two countries' respective quantities (and qualities) of tanks and artillery pieces at the kick-off of Operation Barbarossa.

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Tanks

The German invasion of the USSR, spearheaded by four panzer groups consisting of 17 divisions, had 3,505 tanks at its disposal at the commencement of operations.^1 1024 of these were Pz Kpfw Mark I and II tanks, which were already woefully obsolete by the time of Barbarossa.^2 A further 708 Czech Pz Kpfw 35 (T) and 38 (T) light tanks supported Barbarossa.^3 These tanks, while less appalling than the Mk I and II panzers, were also rendered obsolete in comparison to even outdated Soviet models. All in all, roughly 50% of Germany's tank force consisted of obsolete light tank models - a matter exacerbated by Germany's poor war-time economic management and its relative inability to produce sufficient numbers of newer tank models. German tank production in 1940 averaged 182 units per month, up to 212 units per month in the half of 1941.^4 Keep in mind that this figure includes continuing production runs of woefully outdated Pz Kpfw I and IIs, as well as the swiftly aging Pz Kpfw III and IV models.

In comparison to the above German tank force, the USSR's tank forces were remarkable in both their qualitative (in terms of hardware) and quantitative superiority. A total of 1,861 KV-1 and T-34 model tanks (the newest and most effective in the Soviet arsenal) were stationed in the Western USSR at the onset of Barbarossa.^5 To quote Stahel,

"The qualitative advantage of these Soviet tanks was enormous. In practical terms it meant that none of the German tanks regardless of armamaent could penetrate the armour on the T-34 at ranges above 500 metres. Indeed, only the later models of the Mark III equipped with 5cm L/42 main guns could effectively penetrate the armour of the T-34 at less than 500 metres. The KV-1 was simply impervious to all tank-mounted German firepower as well as the standard 3,7cm anti-tank guns issued to infantry divisions."^6

These ~1,800 tanks were only the newest in the Soviet arsenal. In fact, including the older and far more numerous array of older light tanks such as the T-26 and BT series tanks, there were a total of 23,767 tanks available to the USSR on the eve of war^7 - though not all were stationed in the West, of course. Older Soviet models were far more vulnerable to German tanks and artillery pieces, with typically woeful armour and durability. These models were typically equipped with 4,5cm cannons that were quite capable of penetrating all German tanks at ranges of 500m.^A Additionally, Soviet tank production far outstripped that of Germany by the time of Barbarossa, meaning it was far more capable than Germany of replacing tank losses - a factor which would be of great importance given the enormous loss of materiel in the coming months.

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Artillery

The USSR outproduced Germany massively in the manufacturing of artillery. On the eve of war. Stahel discusses this concisely and in excellent detail, so I'll quote him here:

"The firepower of the standard infantry division in both offensive and defensive action rested largely with its artillery complement. This placed a premium on its ability to be used in as much concentration as possible and be kept well supplied with shells. The width of the front and depth of operations did not afford such beneficial conditions and its overall employment was complicated by the comparatively small number of German guns, and an alarming shortfall in the production of ammunition. Soviet field armies operated some 32,900 guns and mortars of all calibres over 50mm, while the whole Red Army together possessed the startling figure of 76,500 guns and mortars over 50mm.^8 By comparison, the Germans could muster only 7,146 artillery pieces along their whole front.^9 As with their tank forces the Soviets were let down by poor organisation , training and support services, which initially compensated in some measure for the German numerical inferiority.^10 German ammunition shortfalls were most starkly observed in production of armour piercing shells for the infantry and anti-tank guns, whose output was only 50 per cent of projected targets. Batteries of other calibres were likewise affected, although there were exceptions where production exceeded projections."