Grand strategy for the US is made (or the responsibility of) the President with the advice of his NSC. It is published as the National Security Strategy of the US supposedly annually according to the Goldwater-Nichols Act. Because it is unclassified, it is inherently a partisan political document - some more so, some less. (The best of these was the final one published by the Budh 41 Adminsitration.) The NSC includes the CJCS as a statutory advisor; therefore, the military has appropriately input to US grand strategy. Note that the NSS is, in reality, a bureaucratic product so the Joint Staff and OSD are players. Key players from both as well as the NSC staff often wear military uniforms.
All true but that may or may not really become a grand strategy, which to be operational, has to exist as a shared set of assumptions among the broad elite, not just among a few members of agovernment bureaucracy during a particular administration. Cranking out policy docs will not cut it. The grand strategy has to be accepted deeply by the American people, or at least their broad leadership, or it rests on sand.

Containment was a grand strategy. So was the Atlantic Charter. So was the Open Door and the Monroe Doctrine. They were grand strategies because their core transcended normal partisanship and, in practice, became a frame of reference with which partisans and officials understood, framed and debated policy options and strategic goals. The grand strategy represented a vital consensus.

America lacks a real grand strategy right now because it is deeply divided between Left and Right and between elite and masses and few politicians care to do the hard work of building such a consensus or have the longitudinal perspective to see the need to do so. Short term thinking prevails.