Overthinking this topic just a bit.

Garters to hold up one's hose, and keep them from bagging around the ankles, have been around a long time. Lady's and men's fashion have included hose and/or stockings long before modern elastic. If you look at drawings and paintings as far back as the 16th Century you see pantaloons breeches, plus 4's etc. paired with stockings.

What to do, what to do? The folks of those days could wait around for the invention of elastic, but baggy ankles have always been seen as less than well mannered.

There is a line in the record of Captain, Sir Francis Drake's ships stores logs for 50 pair of garter buckles. C. S. Forrester in his Hornblower series makes reference to the Naval uniform including stockings, garters and buckles. The order of the Garter and our own Clan Crests show a strap with a buckle of a type similar to those described earlier.

Ribbons, cords and ties have been used with clothing for a very long time and the use to hold up your stockings is well known. Our modern idea of flashes hanging from an elastic band is probably a fairly modern development. At least since the development of synthetic elastomers. I suppose natural rubber could have been used before. but the point I am trying to get across is that just because we, today are used to elastic with flashes hanging down does not mean that something to hold up your hose was not used before elastic.