Francis Celora in Delta as a Geographical Concept in Greek literature (login required, 100 free articles / month) notes:
That a stranger who arrives at the mouth of the Nile in times when maps were almost scholars' curiosities can visualize the shape of the Delta region and produce the almost witty comparison with a letter of the alphabet is an achievement. This achievement is almost certainly a Greek one, since in the various combinations of Egyptian hieroglyphics which denote the Delta region there are no triangular signs that might ave caught Greek eyes. ... It does not seem likely that they got the idea from the Egyptians. Now the Greek alphabet had been obtained from the Phoenicians and we can learn that the letter delta ..., in a form more or less like a triangle, was borrowed very close to 850 B.C. This gives us the earliest time though it was unlikely that the geographic term was coined as early as that.
Solon, the lawgiver, if we go on the evidence of Plutarch, is said to have visited the "outflows", or "mouths', of the Nile after making his Athenian reforms in the 590's [(BCE)]. His account is in verse, but meter would not have prevented him from using the word delat if he had it at his disposal or if he had wanted to use it.
Herodotus uses the word Delta fourteen times in his History but never as a technical term. it is always the Delta rather than a delta.
This would seem to date the common recognition of the Nile Delta as being triangular shaped sometime between Solon and Herodotus.
Celora goes on to discuss the, somewhat later, migration of the name "Delta" from that of a unique place, at the mouths of the Nile, to a technical term commonly used for any similar rivermouth alluvial deposit regime.
- Celoria, Francis. "Delta as a Geographical Concept in Greek Literature." Isis 57, no. 3 (1966): 385-88. Accessed September 22, 2020. http://www.jstor.org/stable/228368.