God you are a moron. The League of Nations created Israel as part of the breaking up of the Ottoman Empire in the wake of WWI. The USA wasn’t even a member of the League of Nations. The LoN gave the administration of Trans Jordan and the creation of the various Northern African countries to the British along with the French. The British split Trans Jordan into a Muslim Jordan and a Jewish Israel, although the Brits refused to turn Israel over to the Jews until forced to by the UN after WWII, but rather than deporting the Muslims into Jordan, they set internal borders within Israel to create indefensible borders with hostile Muslims enclaves salted throughout what was to become Israel. The USA had nothing to do with any of that.
Wrong.
The League of Nations did absolutely nothing over Israel because it did not at all exist until the UN created it in 1948.
What the League of Nations created was the independent native state of Palestine.
In 1920, the Treaty of Sevres and Treaty of San Remo created the native Palestine in return for the Arab Palestinians helping Lawrence of Arabia to defeat the Ottoman Empire.
And no, the League of Nations cannot and did not give any country to anybody.
The Treaty of San Remo and Treaty of Sevres created the British Mandate for Palestine, but the did not mean the British owned Palestine. Instead what a Mandate means is that the British had an obligation to prepare Palestine for independence.
The reason the UN got involved is that the illegal immigrant, Menachem Begin, blew up the British peacekeepers in the King David Hotel, so no longer wanted any part in it.
But here is Sir Winston Churchill straightening out the false claim of Israel ever being legal.
The Avalon Project : British White Paper of June 1922
{...
Unauthorized statements have been made to the effect that the purpose in view is to create a wholly Jewish Palestine. Phrases have been used such as that Palestine is to become "as Jewish as England is English." His Majesty's Government regard any such expectation as impracticable and have no such aim in view. Nor have they at any time contemplated, as appears to be feared by the Arab delegation, the disappearance or the subordination of the Arabic population, language, or culture in Palestine. They would draw attention to the fact that the terms of the Declaration referred to do not contemplate that Palestine as a whole should be converted into a Jewish National Home, but that such a Home should be founded `in Palestine.' In this connection it has been observed with satisfaction that at a meeting of the Zionist Congress, the supreme governing body of the Zionist Organization, held at Carlsbad in September, 1921, a resolution was passed expressing as the official statement of Zionist aims "the determination of the Jewish people to live with the Arab people on terms of unity and mutual respect, and together with them to make the common home into a flourishing community, the upbuilding of which may assure to each of its peoples an undisturbed national development."
It is also necessary to point out that the Zionist Commission in Palestine, now termed the Palestine Zionist Executive, has not desired to possess, and does not possess, any share in the general administration of the country. Nor does the special position assigned to the Zionist Organization in Article IV of the Draft Mandate for Palestine imply any such functions. That special position relates to the measures to be taken in Palestine affecting the Jewish population, and contemplates that the organization may assist in the general development of the country, but does not entitle it to share in any degree in its government.
Further, it is contemplated that the status of all citizens of Palestine in the eyes of the law shall be Palestinian, and it has never been intended that they, or any section of them, should possess any other juridical status. So far as the Jewish population of Palestine are concerned it appears that some among them are apprehensive that His Majesty's Government may depart from the policy embodied in the
Declaration of 1917. It is necessary, therefore, once more to affirm that these fears are unfounded, and that that Declaration, re affirmed by the Conference of the Principle Allied Powers at San Remo and again in the Treaty of Sevres, is not susceptible of change.
...}
It clearly says Palestine was to be for the native Arabs, and the only thing the Jews got was facilitated immigration into the Arab Palestine.