I can't talk about how camouflage became universally adopted, but I can speak as to why it wasn't, specifically in the Revolutionary/Napoleonic era (1789-1815) in Europe. It's worth remembering that the napoleonic wars took place within the nationalist explosion of the french revolution but the armies still were based on gunpowder/volley-fire with large units. Battles became bigger than ever before in the eighteenth century but the technology remained mostly unchained. The mainstay of militaries were smoothbore (unrifled) muskets and cannon. Just the casualties at Borodino reached ~60,000 in 1812, ~50,000 at Waterloo in 1815, armies could run in the hundred thousand range, and the Grande Armée force in the 1812 campaign reached half a million men. This means that a LOT of soldiers were fighting on relatively small battlefields with weaponry that produced a LOT of smoke. Commanders quickly lost sight of the battlefield and sometimes their own men in the smoke, the bright uniforms and fanciful headgear made practical sense in this type of warfare. What's the point of camouflage if means your own men can't see each other, much less the enemy? Also bright, fancy uniforms allowed units to create an ésprit de corps, especially in the Imperial Guard.

Additionally camouflage makes sense now because weaponry is so accurate if an enemy sees you he can aim at you and the bullet will hit its target. Muskets did not behave like this, not only were they short-range, or produce a lot of smoke, they were incredibly inaccurate.In the words of Gunther Rotenberg,

“According to Prussian tests, the 1782 musket hit a 10-foot wide and 6-foot high target about 60 times out of 100 at 100 paces, only 40 tiimes at 200 paces, and only 25 times at 300 paces...Prussian, French, and British tests indicated that 500 men firing two volleys against an attacking infantry column over a range narrowing down from 100 yards could, in theory, expect to obtain between 500 and 600 hits [i.e. half of shots fired]. Actual combat experience, however, indicated that due to the thick smoke, careless loading, and various malfunctions, the number of hits, at best, ranged between 6 and 15 percent of rounds expended. The first volleys were the most deadly; thereafter effectiveness declined sharply.”

This means that camouflage before the advent of at least rifled muskets, though I would argue even up until the advent of bolt-action rifles and smokeless powder, was effectively unnecessary. Fighting was so close that the enemy is likely to see you anyway no matter what you wear, but even if your unit blended into the surrounding countryside, the enemy regiment would have to fire a huge number of rounds to even hit your unit anyway, regardless if they could see you or not. So because muskets were so inaccurate, and especially because so much smoke was produced, it made more sense to go with bright uniforms even though they were also more visible to the enemy.

Source: E.Rothenberg, Gunther. The Art of Warfare in the Age of Napoleon. Indiana University Press, Bloomington, 1980