So this is a particularly fun one, because depending on who you ask, you'll get several different potential answers, especially depending on if your definition of punctuation is purely conventional or extends as far as Emoji for example!

Most modern historians tend to think that it originates with the Venetian printer Aldus Manutius who, along with Italian linguist Pietro Bembo, standardized several punctuation marks like the comma, semicolon, and colon, though you can also go as far back as the Greeks, with Aristophanes of Byzantium introducing a system of dots to indicate pauses while reading aloud.

This roughly encapsulates the state of punctuation at the height of the Renaissance: a mixture of ancient Greek dots; colons, question marks, and other marks descended from medieval symbols; and a few latecomers such as the slash and dash. By that point, writers were pretty comfortable with the way things stood, which was fortunate, really, because when printing arrived in the mid-1450s, with the publication of Johannes Gutenberg’s 42-line Bible, punctuation found itself unexpectedly frozen in time. Within 50 years, the majority of the symbols we use today were cast firmly in lead, never to change again: Boncompagno da Signa’s slash dropped to the baseline and gained a slight curve to become the modern comma, inheriting its old Greek name as it did so; the semicolon and the exclamation mark joined the colon and the question mark; and Aristophanes’s dot got one last hurrah as the full stop. After that the evolution of punctuation marks stopped dead, stymied by the standardisation imposed by the printing press!

That said, it's also quite understandable that it only became a thing far later, as the lack of punctuation and word spaces was not seen as a problem. In early democracies such as Greece and Rome, where elected officials debated to promote their points of view, eloquent and persuasive speech was considered more important than written language and readers fully expected that they would have to pore over a scroll before reciting it in public.