[coderaptor]

Do we have evidence it was carved?

It’s possible to “shrink” a stamp by pressing onto wet clay, firing, and then repeating the process multiple times (clay will reduce after firing).

I wonder if this could have been etched or pressed, potentially with a chemical process?

[cossatot]

Agate is silica (quartz) and is harder than steel, or any common metal or alloy that pre-modern people would have had. A few common minerals are harder, such as feldspar and hornblende, and modern ceramic is (but not all fired clay). I think tools made or tipped with these must have been used, and/or perhaps finely ground minerals were used as an abrasive polish.

[irrational]

Apparently the stone is very hard and difficult to carve. Presumably this would mean it wasn't pressed in some manner.