Before the invention of written language, so putting a precise date on this is impossible.

Knowledge of silk production implies at least some knowledge of the life cycle of moths (including butterflies). Silk is a protein fiber created from the cocoons of silkworm moths. Unfortunately, silk is prone to decay over long time spans, making determining the start of silk production itself difficult.

According to Chinese legend, silk was first discovered in Henan province around 3000 BC. Obviously legends cannot be treated as historical fact, but an invention of silk in Henan makes sense--silkworms primarily feed on White Mulberry, which widely grows throughout the province. Henan was also a primary population center for Chinese and proto-Chinese cultures for millennia.

Henan is the home of the Jiahu Site, a treasure trove of information on Neolithic China which was recently discovered to hold the earliest evidence of silk production. In 2016 a team of researchers analyzed soil samples collected from graves at the site and identified within them fibroin, the main protein component of silk. The full study is available for free here. These findings suggest a much earlier date for the origin of silk (and by extension, a much earlier maximum date for the discovery that caterpillars turn into moths/butterflies), to sometime between 7000 and 5500 BC.

It is quite possible that the butterfly life cycle was known far earlier--butterflies being found on almost every human inhabited landmass--before silk production came into existence, but there is no way to determine when or where this discovery might have taken place.

It seems like it would be jarring to realize such a drastic change happens to an animal.

Just a minor point, but much of early recorded natural philosophy concerns itself with trying to talk about these kinds of changes. An acorn turning into an oak tree is no less mystifying than a caterpillar turning into a butterfly, for example. The question of how life develops and changes so dramatically (how does a baby become an adult? how does a baby even get formed?) has preoccupied people trying to make sense of the natural world for millennia (and is still a major area of research!). "How do organisms develop over their lifetimes?" is perhaps the oldest question in what we would now call biology (and ends up dove-tailing into much later discoveries like genetics, for example).

Aristotle wrote of caterpillars as being the same question essentially of how all insects turn from grubs into mature forms:

The so-called psyche or butterfly is generated from caterpillars which grow on green leaves, chiefly leaves of the raphanus, which some call crambe or cabbage. At first it is less than a grain of millet; it then grows into a small grub; and in three days it is a tiny caterpillar. After this it grows on and on, and becomes quiescent and changes its shape, and is now called a chrysalis. The outer shell is hard, and the chrysalis moves if you touch it. It attaches itself by cobweb-like filaments, and is unfurnished with mouth or any other apparent organ. After a little while the outer covering bursts asunder, and out flies the winged creature that we call the psyche or butterfly. At first, when it is a caterpillar, it feeds and ejects excrement; but when it turns into the chrysalis it neither feeds nor ejects excrement.

The same remarks are applicable to all such insects as are developed out of the grub, both such grubs as are derived from the copulation of living animals and such as are generated without copulation on the part of parents. For the grub of the bee, the anthrena, and the wasp, whilst it is young, takes food and voids excrement; but when it has passed from the grub shape to its defined form and become what is termed a 'nympha', it ceases to take food and to void excrement, and remains tightly wrapped up and motionless until it has reached its full size, when it breaks the formation with which the cell is closed, and issues forth. The insects named the hypera and the penia are derived from similar caterpillars, which move in an undulatory way, progressing with one part and then pulling up the hinder parts by a bend of the body. The developed insect in each case takes its peculiar colour from the parent caterpillar.

From The History of Animals. I do not mean to imply this is at all the first observation (it is only 350 BCE and surely this was evolved well before then), just an early attempt by a Western philosopher to discuss it.