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I can't speak for everyone, but I believe the peace time professional militaries of most democratic European countries would be dwarfed by the number of people those countries would be able to mobilise in a war time situation.
In the case of Norway, we have a standing army of some 20-30 k soldiers, with a reserve (i.e. peace time civilians with ordinary jobs that have pre-set places to meet up in the case of a conflict) of some 50-70 k soldiers. If shit hits the fan, I wouldn't be surprised if you could get another 100-200 k to volunteer (at the peak of the cold war I believe we had standing army + reserve of some 500 k). The issue is that we are nowhere close to being able to equip that many soldiers.
That's just Norway, one of the smallest populations in Europe, and we would likely be able to field 100 k + soldiers within a week or two, with another 100 k following up in the next months, given that we have the equipment for it.
Call me naive, but I honestly believe that people in democratic countries would be willing to enlist if there is a real threat of an autocratic regime invading at taking over. Given that we have sufficient numbers of well trained soldiers to hold out the initial weeks/months and train those mobilised, and sufficient equipment to give the mobilised, I hope that we would be able to put a solid force on its feet relatively quickly.
Also, just the sheer population of Europe (≈ 450 million in the EU) is so much larger that e.g. Russia (≈ 150 million) that we should collectively be able to field several million soldiers as long as we have enough equipment for it, and enough trained personell to train the mobilised. So I definitely think it's reasonable to focus on building equipment stockpiles in peace time, rather than having huge standing armies.