I found solid evidence that it was used after 1948, and then saw that the phrase was documented in the book "O Jerusalem" as having been used first by a Jerusalem police chief Kamal Irekat, adopted by the infamous Mufti of Jerusalem and then used by Fawzi el Kaukji, an Arab League field commander.
Yisrael Medad looked at the issue and found a British memo from August 1948 from Foreign Secretary Ernest Bevin:
It is quite untrue to suggest that we have let the Arabs down or failed in any obligations towards them. We did not urge them to intervene by force in Palestine, nor did we promise them support if they did so. They went in of their own accord, in most cases without telling us beforehand. Very small measure of military successes which they achieved shows that their forces, while capable perhaps of occupying friendly territory, were not prepared for and incapable of undertaking major military operations, which would have been necessary to achieve the announced object of the Arab states, namely to drive the Jews into the sea.
I wanted to see if I could find an earlier version in contemporary newspapers.
An AP dispatch from June 10, 1948, said that Jews were amused at Arab claims that they already had thrown Jews into the sea:
This article from the News York Daily News in April 1948 quotes Fawzi al Kaukji directly:
An AP analysis from February 8, 1948, uses quotation marks for the phrase referring to Arab leaders in 1947:
The earliest quote I can find is from AP from a December 19, 1947 dispatch, quoting "Arab informants:"
That is a lot of different sources for an identical expression. It sounds like this was a common Arab response to the 1947 partition plan.
Medad also found this cover of an Egyptian pamphlet literally titled "Throw the Jews into the sea" before the 1967 war:
