"Israel's goal was to survive"
You act like in this war the Arabs were trying to delete Israel. That wasn't the case, they only wanted to regain their lost territory. Egypt wanted the Sinai, Syria wanted the Golan heights. Egypt got what they wanted, literally taking what was more than half of Israel at the time. Syria didn't get the heights, but Israel didn't manage to roll into Damascus like it wanted to either.
The Arabs showcased the fact that they were still a fairly potent military threat to Israel, and scared Israel enough to give up more than half of its land.
If the Americans didn't resupply Israel to no end, trust me, the Jewish state would be nothing but a bitter memory.
Israel's goal in all wars was to survive.
The Arabs wanted to destroy Israel, but they knew they could not, so their goal was to return the territories they lost in the Six-Day War.
Prior to the Yom Kippur War, Egypt wanted to negotiate the fate of Sinai, but not for peace with Israel or recognition of Israel,Israel didn't agree. Five years after the Yom Kippur War, Egypt agreed to peace with Israel and recognition of Israel provided that Sinai was returned to it,Israel agreed and signed the peace treaty.
Israel's policy after the Six Day War was "lands in exchange for peace", meaning that Israel would return all the territories it had occupied in exchange for peace.
No country agreed.
After the Yom Kippur War, the Egyptians agreed.
What happened was that Israel managed to achieve what it wanted without it being its goal.
Israel didn't plan to invade Damascus. I will also quote one of the generals, "What do we have to look for there?"
*"The Arabs showcased the fact that they were still a fairly potent military threat to Israel" - This is true.
*"and scared Israel enough to give up more than half of its land." - That's not true and I've already explained why.
American aid began to arrive only when Israel became the winning side in the war, and the airlift arrived as Israel already encircled the Third Army and succeeded the Suez Canal.
The American aid didn't affect the course of the war too much.
Egypt and Syria had no chance of destroying Israel even without American aid.
You also forget (apparently on purpose) that the Soviet Union shortly after the war began, began to send a massive airlift to Egypt and Syria, before the Americans, and much larger than the American one.
Add to this the threats of the Soviet Union to Israel, that if Israel will not stop its progress then the Soviet Union will start a war against Israel.
Don't forget that as soon as the momentum moved to Israel, the Egyptians asked for a cease-fire, and Israel didn't agree.
In addition, the Egyptians asked the United States to intervene in their favor.
This war caused the entire Arab world to understand that even under perfect conditions they can not defeat Israel, which led to decades without wars and peace agreements.
The stupid State of Israel managed to achieve something without intending to achieve it, which is exactly what happened in the Six-Day War.