For most people this looks like a very easy question: in 2001, when the Agile Manifesto was published. The first comment to this is that the "Agile Manifesto" is in fact the manifesto for Agile software development and while it is very important in the Agile history it is not the beginning.
Like many other discoveries "Agile" was originally a byproduct of military advantage. The first mention of an Agile approach is a study from the United States Department of Defense in late 50s aiming at finding ways to adapt military supplies to the specifics of war zones. It was the start of the Agile Manufacturing, and in my opinion manufacturing is still ahead in terms of agility.
In the big scheme of things, like history, software development is a new topic. People "uncovered better ways" of doing it for millenia. Since we were hunters there were people that thought "out of the box" even when there was no such thing as a box :). The difference was the rate of change, thousands or even hundreds of years ago the society was pretty conservative and "new ways" were considered dangerous and sometimes crazy.There was no need for change as it is today.