i have no military background, but if it's anything like civilian government, all the mid- and low-level decisionmaking is done by apolitical career professionals. and even though the upper management are political appointees, the policies they actually implement tend to have much more continuity from one administration to the next than people outside the government imagine. ... it's also true that, from the PoV of people at the top, the executive branch has a surprising amount of inertia affecting how and when and whether it does as it's told.
that said, the high level decisions, such as whether to start a war, and the broad strokes within that, are made by the president and his appointees.