Alcohol production was one of the earliest things humanity learned to do and seeing as how flammable it is I doubt alcohol fires were uncommon. So I think it would be pretty reasonable to expect somebody to put two and two together to produce a Molotov cocktail, but I've never read about them. So what gives? Did people just not think about it. Were vases/bottles/jars too pricey? Or did somebody do it just to discover that it was kinda worthless at the time?
There have been regular questions here about Greek Fire, a loose term for what were likely a number of different fire weapons tried by the Byzantines in naval warfare. A good answer ( with links to good articles) is here . While delivery methods were not the same ( for one thing, big glass bottles would not have been cheap) the idea was the same, getting a burning substance onto an enemy's craft and disabling it. And, like Molotov Cocktails, it was limited in how it could be used and likely also not very difficult to defend against.