You are VASTLY underestimating what can be done by nations when they put their efforts toward raising an army.
Some quick historical parallels......
Confederate States of America
Population: ~5,500,000 (Caucasian)
Army Size: 1/1861 = 0
12/1861 = ~500,000
England WWII
Population: 46,000,000
Army Size: 1/1939 = Regulars 227,000/TA 204,000
5/1940 = 1,650,000
April 1940 BEF strength 400,000
Australia WWII
Population: 7,039,000
Army Size: 9/1939 = 80,000
8/1942 = 479,000 11 Divisions
Russia: 6/41 303 Divisions
8/41 401 Division (with 41 destroyed)
Russia was in effect shitting divisions in the first months of the war; about 5,000,000 men by December if memory serves me correct.
What you can see from these quick examples is that manpower is hardly ever the issue in effect for rapidly raising a force. A rough rule of thumb; you can effectively double the size of your military within six months from the decision to mobilize. Now that does not mean that you will have units every bit as good as those that existed pre-mobilization, but it does mean you can get an adequately trained and effective combat force into service within 6 months. US Cold War planning assumed about six months to fully mobilize from about 15 divisions to 35 divisions within six months. Desert Storm was the first real test, as it tried to mobilize three National Guard brigades within 60 days. That attempt did not work out as planned, as these units still required considerable training to get them up to active duty standards. However, it was conceded in post-war studies that the three brigades could have deployed and been effective at the 60 day point; just not fully trained to active duty standards. It was also conceded that at least one of the units was indeed fully qualified, but somewhat arbitrary training rule said it was not, and that if the decision had been to go ahead and deploy, training deficiencies could have been addressed in country after deployment and the units rated as fully ready by the start of the war.
In any event, your main limitation is equipment. BUT that is not really an issue for small arms, as doubling production for say the M-16 or the AUG can be accomplished in a few weeks. Australia in 1995 had thousands of L1A1s, Sterlings, Stens, and Brens in storage. And then there are wartime production plans. Normal production for most arms manufacturers are basically one 7-5/M-F shifts. Wartime, it goes to 3-shifts 24/7/365. Just look at WWII production in the US and UK at what can be accomplished. You had workers all but being dragged off the streets and stuck on a production line. In Russia, that was literally happening. Its also interesting to note that in 1990, the US expected to reactivate B-1B production within six months of a decision to do so. Wartime production plans for F-16s hit over 600/yr within one year. M-1 production was to be doubled as well.
The hallmark of mobilization for war is to not start off thinking about what you can't do and concentrate on doing what you must do. The US built the atomic bomb in three years. It built an army of 8,000,000 in less than four years. Australia itself went from an army of 80,000 in 1939 to 479,000 in three years. Its all a matter of national will.
For the record, I was a logistic officer in the Air Force.
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