“It will be on that day, a Great Shofar will be blown and the lost from the land of Ashur and those banished to the land of Egypt will come, and bow to God on the Holy Mountain in Yerushalyim.”
When the Shofar is blown on Rosh Hashanah this inspires the inner heart (intent) of the Jew to turn to God, which reciprocally creates the reverse.
The Great Shofar that will draw the heart of the Jews at the time of Moshach actually is greater than the regular Shofar – which emanates from Sovev Koil Almin – it comes directly from G-d.
The reason we blow not Shofar on Shabbos is because the Shofar aruoses God’s pleasure in creation whereby on Shabbos this pleasure (to some extent) is already present.
The reason why nonetheless, though it was Shabbos, in the Beis Hamkdosh the Shofar s blown, is because as there are many levels to pleasure, hence the pleasure elicited by the Shofar blowing in the Beis Hamikdosh is superior to the Shabbos pleasure.
The Great Shofar that will be blown when Moshiach arrives is greater than the Shofar blast heard at Mount Sinai.
The difference between the two is whearas at Matan Torah the Jews already were inspired, hence a regular Shofar could arouse their heart, to those lost in Ashur and banished to Egypt (distant Jews) it needs the Great Shofar.
Every single thing in the Torah – Torah comes from the word Horah / life-lesson – is!
The reason one side of the Shofar is small and the other wide as the verse states “From the constraint I called to God – Please Answer Me With Expansiveness.”
There is as mentioned the prayer of the wealthy and the prayer of the poor, whereas the prayer of the poor is deeper, hence the reward is more appreciated.
Similarly the prayer of the poor – from constraints – arouses the infinite expansiveness.
This too is the meaning, that every year that begins poor, ends rich.
This also means (not necessarily literally, rather) that the Jewish people make their prayers in humility.
This is the meaning of the arousal of the great Shofar in the era of Moshiach – as the Jews are in difficult constrains, this arouses the depth of Divine love (compassion.)
As such we see a a connection between the Shofar of Moshiach (from when the Jews are in constraints) to the Shofar of Rosh Hashanah.
Rosh Hashanah has two general themes – a. it is the day of creation of man b. it is the day of the elevation of the universe.
The entire purpose of the descent into exile is to cause this constraint which evokes God’s essence hence elevating – to a higher level.
The entire purpose of creation – which is called a secondary reason – is for the primary reason, the Jewish people.
Now it need not be the Jews are in actual constraints in the beginning of the year, for it to follow in prosperity, rather a Jew may be complete (physically and spiritually) but by humbling oneself, this does the trick.
The way we humble ourselves (even when we are “complete”) is by realizing that all – especially spiritual – that we have achieved is actually only Divine compassion/grace.
A Jew must feel that whatever s/he has accomplished is not due to my greatness but God’s enabling.
This (humility) that all I achieve comes from (God) not only doesn’t weaken one’s resolve and effort, it in fact increases it.
When a person assumes that they are the cause of their successes, they are limited by their assumed abilities; but when one understands that their successes come from God, this unshackles their limitations.