If you're talking about the western European dress tradition, the earliest bangs that I'm aware of would be from the early 17th century. That's when we start to see occasional tight, short and then more danggly curls across the forehead. Later in the century, this became light, wispy curls or more defined ones. However, a clean hairline was much more common in portraiture through the entire century.

In the later 1780s, fashionable women's hair was cut with a lot of layers and curled, which could result in a kind of bang-like style. But the hairstyles of the 1790s show many more actual bangs, whether fluffy and feathery, long and curly, or more modern and straightish. The latter two remained fashionable for the first couple of decades of the 19th century, though usually parted, and in the 1810s there was also a trend for flatter curls across the forehead. These soon went out of fashion again, and bangs didn't come back until the late 1870s - they can be seen worn sleek and smooth, but really frizzy ones were quite fashionable. (Some photographic portraits show feathered piles that look like they could have come out of the 1980s.)

(This is why "when did people start to wear X" questions are so difficult - there are outliers in every period, and there are a lot of practices that have been picked up, discarded, picked up again in a different way, discarded again, and then reinvented.)