According to the Palestine Football Association, Palestine was the first Asian Arab team to participate in international competition. They are of course referring to the 1934 and 1938 World Cup qualifiers.
In 1928 the Palestine Football Association was established in British Mandate Palestine. To figure out who this organization really represented, one could take a look at the squad lists that participated in the Greece and Egypt qualifiers and notice that there is not a single Arab name. The truth about the mandate era Palestine Football Association's inception is that it was part of a larger Zionist attempt to gain international legitimacy for Jews in Mandate Palestine and consequently, Arabs were deliberately left out of the teams fielded. And the reason Egypt played a Zionist team was because they were under a British mandate as well. For further reading on this: a great article by Issam Khalidi.
Both the Israeli and Palestinian FAs lay claim to the pre-1948 matches and list their establishment dates at 1928. So which of the modern associations is the rightful successor of the mandate era association?
FIFA took its usual neutral stance on the issue. It has recognized both the Israeli and Palestinian FAs as being established in 1928 and according to the FIFA.com archive, both teams played their first matches in 1948 and 1998 respectively (it used to be that the Mandate games were in the archives of both teams).
To me it doesn't feel right for us to recognize the mandate FA as our own simply because that association was Zionist in essence. Then again, allowing the Israeli FA to have exclusive claim over it fulfills their political goals (technically the team was supposed to represent BOTH Arabs and Jews and not be exclusionist). Thats why I think the FIFA position is the best to take.
We openly accept the mandate team as our own so as to highlight how established football is in Palestine and in light of the above facts, you can legitimately ask whether we are deluding ourselves. My answer to that is no. While we did not have an Arab international team per se, football has a long history among Arabs in Palestine that predates 1928. The established clubs in Bethlehem, Jerusalem, Gaza and elsewhere prove this.