Is it true that people living in "the Old Testament" period were saved by faith in a coming Messiah?

Hebrew Scripture is all about “Sowing and Reaping”; thus, if we repent of the evil we have intended against God, God will likewise repent of the evil He has intended against us (Jonah 3: 10)

From whence do we know that repentance (and turning away from evil) is the way to have our sins removed? We know it from the verse that goes on to say: «As far as the mizrach (east) is from the ma’arav (west), so far hath He [God] removed peysha’einu (our transgressions) from us»- Psalm 103: 12.
Where are “East” and “West” Located? And, how far is the East from the West? The answer to this question is that “East” and “West” are no particular locations, but rather opposite directions which we willingly choose to follow. In other words, we could be heading East, yet in the moment we stop, and make a 180 degree turn (in order to start traveling in the opposite direction), we have thereby bridged the gap covering “the distance” between East and West.
And that’s exactly how God removes (pardons) our sins-- they are removed the very moment we recognize we are heading in the wrong direction (away from God, with our constant transgression of His commandments) and choose to make a 180 degree turn [in order to start walking in the opposite direction].
This 180 degree turn is what we normally call “sincere repentance”- to have a contrite heart; to abandon evil, and to start doing good. This is God’s true sacrifice; not that of a human Messiah, nor that of any animal beast, but the sacrifice of our selfish ego (our “Yetzer ha-ra”, or “evil inclination”). And this is why Scripture goes on to say: «For you don’t want sacrifices, or I would give them; you don’t take pleasure in burnt offerings. My sacrifice to God is a broken spirit; God, you won’t spurn a broken, chastened heart»- Psalm 51: 16-17;
And also, «Hashem is near unto them whose lev (heart) is broken; and saveth such whose ruach (spirit) is contrite»- Psalm 34: 18; And still in another place: «With what can I come before Adonai to bow down before God on high? Should I come before him with burnt offerings? with calves in their first year? Would Adonai take delight in thousands of rams with ten thousand rivers of olive oil? Could I give my firstborn to pay for my crimes, the fruit of my body for the sin of my soul? ” Human being, you have already been told what is good, what Adonai (God) demands of you - no more than to act justly (with your fellow human being), love grace (doing mercy) and walk in purity (humility) with your God»- Micah 6: 8.
Thus, mankind redemption doesn’t come from any human Mashiach, but rather from sincere repentance. In fact, it could be validly said that repentance is [in itself] God’s true Mashiach, as it is taught in the verse that goes on to say: «And the Go’el (Redeemer, or Mashiach) shall come to Tziyon, and unto them that make teshuva (sincere repentance) and turn from peysha (rebellion) in Ya’akov, saith Hashem»- Isaiah 59: 20.
Notice how the verse doesn’t say that Mashiach will come unto those who believe in him, but rather unto those who make Teshuva (repent). Why? Because “Teshuva” and “Mashiach” are actually the same. And the former is also confirmed by a Jewish Midrash (Sanh. 98a) that promises that Mashiach will come TODAY... “if we hear His voice, and Harden not our hearts... (in other words, if we proceed to sincere repentance)”- Psalm 95: 7-8.

«A Religious text, taken out of it's Historical context, is a poor Moral pretext»

Is it true that people living in " the Old Testament" period were saved by faith in a coming Messiah?

When it comes to inspire and uplift, faith in a coming Messiah can be a powerful tool. The only problem with the idea of Old Testament people being saved by " looking forward to the Messiah" is that it seems to be sort of " disconnected" from Bible's own narrative.
In other words, Hebrew Bible doesn't record even one single instance where any person [whether he be Hebrew or Gentile] was ever condemned by God for the sin of refusing to believe in a coming Messiah. Yet, Hebrew Scripture provides numerous examples of specific people being punished for refusing to obey God's commandments [as well as people being rewarded for their obedience to them].
Of course, we recognize that at the end of the day, " the tree can be known by it's fruit". So, if your individual theology concerning Jesus of Nazareth [peace and blessings be upon him] brings you peace and deliverance, it would be wise for you to hold fast to it. As for ourselves, we can't find inner peace following any sort of theology that would leave us feeling as if we are not being completely honest with ourselves (with that which we sincerely believe to be Divine and objective truth), thereby making us liable for violating the Divine command that forbids us from bearing a false witness.
As is written, " Keep thee far from a false matter... " - Exodus 23: 7, King James Bible. And also says, " These are the things you must do: Speak truth to one another; make true and sound decisions within your city gates" - Zechariah 8: 16 (Christian Standard Bible).