What you're describing tends not to describe sedentary state societies, which rely to a greater or lesser extent, but always a substantial one, on specialisation of productive labour: you simply cannot afford to uproot your farmers and/or industrial workers and still sustain a economy, and the skills involved in farming and industrial work do not directly translate to military skills.

However, pastoral nomadic polities did more or less achieve a state of affairs where all able-bodied (typically but not invariably male) members were fully militarily capable, which emerges out of the ecological pressures of the steppe and consequent sociological effects on its inhabitants. This answer and this answer discuss the causes and limitations of what is termed the 'nomadic military advantage' already, but I do want to restate the key aspects here as relates to your question.

The steppe is broadly non-arable, but extremely well-suited for the grazing of livestock, and has significant pockets of game. As such, nomadic communities have historically been able to thrive in the region by migrating seasonally through areas of pasturage and living on a meat-heavy diet from a mixture of livestock ad game (though invariably supplemented to some extent by grain and other plant-based foods from sedentary communities through trade, raids or tribute). This has a few critical implications:

1. There is very little specialisation of labour, with all members of the community broadly involved in similar tasks;

2. Those tasks entail a lot of riding and a reasonable degree of archery; and

3. The community(ies)' resource base is basically entirely mobile, and requires little labour input to sustain.

This means that a nomadic polity can, practically speaking, mobilise its entire able-bodied (typically but not always male) population for warfare without compromising the integrity of its economy; this population would also be broadly suited to warfare due to being 'trained' as a side effect of their lifestyle and means of subsistence. It is worth stressing, though, that this is a unique product of nomadic polities (not necessarily exclusively Eurasian ones – some historians of indigenous North America like Pekka Hämäläinen have argued that the Lakota and Comanche, among others, can be argued to have developed similarly to Eurasian nomads after the introduction of the horse). We're not talking about a state that has formally decreed that all its population must be trained for war, but rather societies that have organically developed mechanisms that are, by coincidence rather than design, extremely well-suited for pre-modern warfare.