Probably the same way glass is made today. Get a clay or graphite (both can withstand high temperatures, and can be shaped easily) two-part mold in the size bottle you want. Using a known quantity of glass, (you can just weigh it) you clamp the mold around it and blow it. The air forms a bubble in the glass, which becomes the inside of the bottle. And the walls of the bottle quickly cool and harden (holding the shape of the bottle) when they hit the inside of the mold and it begins sapping the heat away like a heatsink. And since it was a known quantity of glass, you know how much volume inside of the mold is taken up by glass (and inversely, you know how much is taken up by air, which determines the bottle’s volume.)

It’s basically injection molding, but using air to fill the space instead of just injecting glass into the entire mold.