The difficulty here is that, historically, the 1939 Red Army was a mess. Sure, it was already massive, but it was only partially mobilised, it didn't have enough tanks to fill it's mechanised corps, let alone enough trucks, and the tanks it did have were mostly light cavalry tanks and outdated machines like T-28's. Then we come to the fact that between 25% and 50% of officers had been relieved of duty or, even worse, executed between 1937 and 1939. (about 30% of those that were purged from the army ended up being re-enlisted during WW2, but they would definitely be missed during the initial phases of the war). The Red Air Force wasn't in much better shape, with the most modern fighter fielded in any significant numbers being the Polikarpov I-16. Supply transportation would likely have become a big issue for the Reds as soon as they started to make some inroads. Bear in mind that the railway gauges are different and changing standard gauge to Russian gauge is problematic because the ties aren't wide enough, so it requires a lot more effort than the reverse. Lend-lease lorries were the backbone of Soviet logistics in 1944-45, when they were fighting in Germany, and without the US in the war, and the Brits still working to supply their BEF, there is no way they would have enough lorries. This means that any Soviet advance into Poland/Germany would be slow and fraught with logistical difficulties. A difficult variable to quantify would be the German response. I suspect that it would depend on the timing. If the Soviets declared war immediately after the fall of Poland, the Wehrmacht might go on the defensive on the Western front and use it's panzer forces to take a chunk out of the woefully unprepared Red Army. If war is declared a few months later, when the Panzers have already been relocated to the Western Front, the Germans might panic and start sending Panzers back east immediately, or they might do what they did historically and take out France first. I would expect the Germans, due to their ideology and assessments of the time, would ignore the Soviets at first as they would see the Western Allies as a much bigger threat, especially if the Soviets get bogged down early on due to mud, logistics, and general organisational chaos. This is both a blessing and a curse for the Soviets, who would have an opportunity to make some inroads into Western Poland and get themselves somewhat organised, but they would soon run into logistical issues. Attrition of the badly led and inexperienced front line units is bound to be a problem even if the Soviets would have local numerical superiority initially. This would be more of an issue of not being able to send reinforcements to the front quickly enough, rather than a manpower shortage. Over time, of course, the Soviet industrial machine would kick into gear, officers would be called back from forced retirement, experienced troops from the Far East would be brought over, reserves would be called up, and things would get organised, but this would take a lot of time, time which the Wehrmacht might just use to launch a few major offensives not unlike the ones it did historically, and who knows how effective those would be at prolonguing the war. It's also possible that the Germans wouldn't invest quite so much air power into the battle of Britain, rather taking a defensive stance in the West, and using most of the Luftwaffe's strike power on the Eastern front, against the woefully underequipped and undertrained VVS.
I wouldn't expect a quick victory for the Soviets in any case, but eventually, I suspect they will succeed. Of course, one wonders whether the morale of Soviet soldiers and civilians would not have been affected by the fact that it was Stalin's regime that dragged them into the war instead of a brutal surprise invasion by a ruthless enemy that was out to destroy them. Soviet Industrial production is also an interesting variable. If they get a few extra months of wartime production before they're forced to relocate eastward, the Red Army's equipment situation might have been drastically different. Of course, they wouldn't be producing T-34's or SVT semi-automatics, but they would have produced a lot more stuff before the relocation, allowing them to be more agressive in counteroffensives to frustrate German encirclements. Now, the difference wouldn't have been as dramatic as one would expect, as Pz.III's were still relatively rare in the German tank forces in 1939 and early 1940, and against a Pz.II, a BT-5 or BT-7 isn't hopelessly outmatched as it would be against a PzIII.
A further impact of this is that the Germans likely would send fewer troops to help out the Italians in Africa and the Balkans, but the Italians would potentially not send as many troops to the Eastern front either, at least initially. This would potentially lead to an earlier Italian defeat in North Africa, and a very bloody war of attrition in Greece, effectively sapping Italian prestige and manpower at an alarming rate. Now, depending on how the Western and Eastern fronts go, German force might still be sent in to 'save the day', but I suspect the Italians will have taken more losses before that would become the case.
If France doesn't fall, be it thanks to a boost in Allied morale, and/or a German knee-jerk reaction to the threat to the East, that changes everything, and suddenly WW2 would start looking a lot more like WW1 as the Wehrmacht divides it's tank forces between the Western and Eastern Fronts, their spearheads would be weaker, and more easily frustrated, the same goes for their Air Power, which would be much less overwhelming than it was during the French campaign, if it were split between two fronts. If both fronts turn into a war of attrition, the German manpower pool, and it's resources, would be whittled down even faster than historically, and eventually, the third Reich will implode under the strain, as it did historically. In this case, the war would likely be won sooner, perhaps as early as 1943 if the US puts in place a large scale lend-lease programme by 1941, and it sends over some troops near the end.
Now, the ramifications on the other side of the globe could go in a lot of different directions. Will the Japanese stand idly by, or will they strike their agressive Soviet neighbour while it is distracted? Will the Japs join the tripartite pact in 1940 if Germany isn't doing so well in it's two-front war? If they don't and maybe even step out of the Axis, will they concentrate on the Chinese and /or Soviets, or will they hit the US anyway? And if they hit the US but they're out of the Axis, will the US ever join the war in Europe? Might the US even support a Japanese war against the Communist Threat, if there is a ceasefire in China?
Of course, there is the additional question of whether the Soviets declare war before or after Poland has fallen. If they do so before, they risk getting bogged down in Poland for a while as Poland would never willingly let the Soviets into their territory, not after the Soviet-Polish war of 1919-1920, and potentially the Polish army might concentrate it's forces on the Soviets rather than the Germans, or split it's forces evenly, as opposed to having most forces face the Germans and then trying to hold off the Soviets with token forces after they declare war over two weeks later.