@deborahh that phrase feels off
the oldest writing system, cuneiform, was written first and foremost by pressing a stylus on clay, with carving in stone reserved for exceptionally important documents.
Hieroglyphs followed soon afterwards, and indeed some of the earliest examples are carved in stone, but they are also small bits of text in the middle of a decorative design, and there are also similar examples that are painted on pottery, which would only require one hand.
Chinese oracle bone script were, like the name says, carved in softer material (bone).
And I don't know whether we know on what surface Maya script started, and I suspect that if it was done on perishable materials we'll never know, because the climate there is quite different from that of Egypt.
And the direction of writing of those early examples varied wildly, even in the same script, with left to right, right to left, top to bottom and even boustrophedon.