Donald Trump and Dana White walking out from the Oval Office before the UFC fight at the White House looked flawless ... but it almost didn't turn out that way ... according to new behind-the-scenes footage that just surfaced.

Fox Nation is releasing a two-part documentary series Thursday titled "UFC Fight House: The Making of the Biggest Fight in History" ... and it captures the interaction between the two powerful men before they head out to the South Lawn for UFC Freedom 250.

Check out the clip ... a coordinator is explaining the timeframe to the pair and taking into account weather issues which nearly derailed the day.

Dana looks nervous before walking out ... while DJT looks calm and in control -- though the two do switch sides, possibly so photogs can catch the Prez on his good side.

The UFC honcho mentions during an interview that, between standing with the president and watching the jets fly over the event, he felt a lot of emotion right before the bouts began.

These moments and many more will be shown in Fox Nation's new documentary, "UFC Fight House: The Making of the Biggest Fight in History," which premieres Thursday, July 2.