The first time was in 1934.
Egypts' El Watan has a story about how the Egyptian team of 1934 played in Tel Aviv.
The team had two qualification matches against the British Mandate Palestine team in that year. In the first, Egypt drubbed the Palestine team 7-1 in a match in Cairo. The followup game in Tel Aviv was on April 6, where the Egyptian again won, 4-1.
The article notes that there was not one Arab on the Palestine team. It claims that there were 6 Jewish players and the rest were British, although from what I can tell the team was exclusively Jewish.
From Wikipedia:
Football was introduced to Palestine by the British military during its occupation of the territory in World War I. (Actually, there were Zionist teams as early as 1906, h/t Yoel.) After the war, the sport's development was continued by "European Jews who had been exposed to soccer in their native countries".[2] Palestinian Arabs, specifically those of Islamic beliefs, refrained from participating in football's early formation due to their resistance to "Western cultural institutions".[3]
The Eretz Israel Football Association was founded in August 1928 and applied for membership in FIFA. It was accepted to FIFA on 6 June 1929 as the Eretz Israel Football Association.[4][5] It was the first of 14 sports organizations which absorbed hundreds of leading sportsmen who immigrated in the wake of antisemitism in Europe.[6]
Mandatory Palestine end up playing five international games before the end of the British Mandate in 1948 which resulted in Israel independence. During those five games, the national team fielded only Jewish players. Three anthems were played before each match: the British "God Save the Queen", the Jewish (and future Israeli) "Hatikvah" and the opposing team's anthem.[7]
In 1948 the team became, officially, the national team of Israel.
UEFA says that the original name of the association was the " Eretz Israel – Palestine Football Association."
The El Watan article notes that the current Palestine Football Association claims to have been founded in 1928, implying but not spelling out that they claim to have have some connection with the Eretz Israel Football Association.
Interestingly, an ESPN article from 2014 about the Egyptian team of 1934 - written by a South African correspondent - falsely claims that the Palestine team had "a majority of British players." Here are the names of all the players of that team:
| Player | Position |
|---|---|
 Willy Berger | GK |
| Avraham Reznik | DF |
| Pinhas Fiedler | DF |
| Zalman Friedmann | MF |
| Gdalyahu Fuchs | MF |
| Yohanan Sukenik | MF |
| Amnon Harlap | FW |
| Perry Kraus | - |
| Paul Kastenbaum | - |
| Haim Reich | - |
| Avraham Nudelman | FW |
| David Weinberg | - |
| Yaacov Levi-Meir | - |
| Yaacov Zelibanski | - |