It depends on the country. In one week, neither France nor the USA has been involved in any war (until today for France) but Romania or Indonesia seem to be involved in some war or another every day.
Plus, France sends the foreign legion to fight in various battles in support of allies or such things. I suppose that other countries do the same, hence that if you’re a good soldier in a not too small country, you might be fighting very often, even if your country isn’t actually at war.
I suppose small countries don’t fight any war, generally, except when they’re conquered. But we haven’t been playing for long.
There are also many countries that are technically at war with each other even though they don’t actually fight. They just never signed a peace treaty. The USA and France have been at war for months, for instance.
I assume it would be possible, if you manage to have its population grow (either by immigration or by conquest). Indonesia is a small country in real life, and she’s now holding a large chunk of Asia and IIRC most of south-Africa and Australia. So, they probably managed to do exactly that.