Well we can start with the obvious basic fact, that the military has been a participant in a vast number of parades not directly linked to an ongoing conflict, or recently ended one, and that includes the 4th of July.

It just usually takes the form of a ceremonial marching contingent, assorted bands, and maybe some mounted cavalry when time and location appropriate. Instances with more broad participation, with towed artillery, armor, support vehicles, and timed flyovers, etc are far less common, and typically very context dependent. Things like the 1946 WW2 Victory Parade in NYC, or the Gulf War parade, or IKE and JFK's inaugurations as the Cold War escalated are good examples here.

Nor is this a new trend, and has as much philosophical origins as practical. Remember the Founding and Framing generation were not generally big fans of standing armies, many could still remember Boston under British occupation before the Revolution, and of course the actual war itself. Even those that did support a regular force werent looking for a large one. Thus local militia units played a far larger role in public celebrations, reviews and parades, gun salutes and all that with the role still today carried on by many communities having local National Guard units in their own small parades for 4th of July and other holidays. So another aspect of military participation in public celebration but one reflective of the fact that for 150 years the US Army was relatively small, not concentrated near major urban centers, and institutionally not occupying the same respected central space it does today.

We should also draw a distinction with the Fleet Week celebrations around the nation annually, which were in essence semi organized celebrations that the Navy decided to officially support in an attempt to better shape their public image. As while a ship at a dock is less worrisome to the American sense of distrust of an motives of an overt military display, its also much easier to forget about and ignore. And again the modern iteration of FLeet Week, with the big ones in NYC, SF, and other cities only took off in the early 80's amidst renewed Cold War tension and the 600-ship Navy initiative. And a similar story with the air shows many bases host each year, a cool jet just doesnt hit the cultural sensitivity to an assertive military domestically that tanks rolling down main street in peacetime do.

So yes there has been at least military participation in many public celebrations including the 4th, going back to the early national history, but rarely anything more than a ceremonial contingent, and usually as just one of several organizations participating. With exceptions being very context heavy.

The Smithsonian did a nice article tracing the history of Presidential participation w/respect to the military in 4th of July celebrations recently, and it also has a few quotes with regards to the Gulf War parade. Showing that for that event too there was concern about its use not as a celebration of the American fighting men and women, but as a tool of political optics as President Bush geared up for a reelection campaign. https://www.smithsonianmag.com/smart-news/how-military-parades-us-have-changed-180968102/

One of the biggest military parades in American history happened at the conclusion of the Civil War following the assassination of Abraham Lincoln. It was called "The Grand Review of the Armies" and happened in Washington DC in May 1865, a month following Lee's surrender to Grant at Appomattox. Around 150,000 Union soldiers from the armies of the Tennessee, the Potomac, and Georgia under Sherman and Meade marched for two days in front of approximately 250,000 spectators, with Grant, Johnson and his cabinet present for the festivities. The armies had to be quickly mustered from active service on the front back to DC to take part in the grandiose spectacle. With the uproarious celebration occurring in the wake of Lee's surrender at Appomattox being quickly overshadowed by the shock of Lincoln's assassination and Seward's near assassination, the government wished to restore post-war morale to the nation with a massive military parade reviewing the victorious armies. It can rightly be called one of the biggest national exhibitions the United States had ever executed at that time.

The New York Times wrote this column on the first day:

"The weather to-day was everything that could be desired for the unprecedentedly grand review of the Army of the Potomac. The atmosphere was pleasant, the sun shone with unclouded splendor, and the recent rains had laid the dust, putting the streets in good marching condition. Thousands of persons, including many from other cities, who have specifically come hither to see the pageant, line the sidewalk from the Capitol to the Executive mansion, a distance of a mile and a half, while windows and balconies, and all eligible positions, including house-tops, were occupied by deeply interested spectators... The general idea is that the number of troops comprising the Army of the Potomac, reviewed to-day, is about seventy-five thousand. No negro troops were in the procession. From the portico of the Treasury Department to-day, the flag of the Treasury Guard Regiment was displayed, the lower portion tattered and torn, not by battle, but by the spur of Booth, the assassin, as he jumped from the box at Ford's Theater to the stage, on the night of the assassination. A placard appended stated this fact, and it attracted much attention."

I'm not sure if this exactly falls into your criteria, but it happened about a month following the generally accepted conclusion of the war with the intent of fostering public morale and national unity.