That is not the ruling Likud ideology in Israel nor the allied national religious ideology; both refer to Israel+Palestine+Golan as "the Whole Land of Israel".
And in any case, the "most religious" (ie those whose politics are most totally driven by Judaism) bloc in Israel are at best ambivalent about the Israeli state and the settlement enterprise, and actively hostile to military service.
Israeli hostility to Iran is driven by a "defensive" paranoia, not a religious mission.
Of course it needs to be approached pragmatically. If Israel stated that its number one goal is to rule the entire region, they wouldn't have been as successful as they are.
Also God didn't say when. But he did promise, according to the Book.
Israel literally has minted coins with the image of Greater Israel (they claim this is only in reference to some ancient coin designs). The US ambassador to Israel, Mike Huckabee, has just a few days ago given an interview where he explicitly stated that Israel / the Jewish people has a right to that entire land, from the Euphrates to the Nile. The Israeli opposition leader was then asked about this, and he agreed with the US ambassador that yes, they do have this right, but that of course it must be viewed realistically given security and operational limitations.