First and foremost you need state-centralised power, rather than the extremely power-diffuse reality for much of Europe in the Middle Ages. You can see this centralisation happening in France, for example, in the 1300s and 1400s with more and more power being assumed by the crown and parlement. From there you enter into the whole 'military revolution debate' of Michael Roberts, Geoffrey Parker and Co. (Clifford Rodgers' edited volume The Military Revolution Debate gives a fantastic account of this from many different perspectives). Basically, state-centric finances (taxation) and military force yield stronger European states that can wage war as a unit, rather than as a collective of smaller units (Barons and Dukes, etc.) that have to be coerced or cajoled into action.
So, 1648 is a useful date because the 30 Years War sees the last of the major, privately sponsored armies in Europe (under Wallenstein, if I recall correctly....it's been a while!), and the state-centric model is largely predominant by the early-to-mid-1600s. The idea that it is a creation of Westphalia, however, is simply incorrect. Again, read the treaty. If you can find where it creates the modern state system I'll be very impressed.