The "T" matters because all have sinned and there are none that seek the face of the Lord.
If there are none that seek the face of the Lord, how do we find Him? The answer is a hard one - for me it was the most difficult of "TULIP".
If we, in our sin, do not have the ability to seek after God, then it must be God that seeks after us.
That is the "U" - unconditional election. Predestination.
Blessed be the God and Father of our Lord Jesus Christ, who has blessed us in Christ with every spiritual blessing in the heavenly places, even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love he predestined us for adoption as sons through Jesus Christ, according to the purpose of his will, to the praise of his glorious grace, with which he has blessed us in the Beloved (Eph 1:3-6 ESV)
Logic tells us that if we are steeping in the "T", we cannot seek God. We are chosen in Christ.
Our election is not based on the good that we have done - it is unconditional upon our behavior.
It is the very idea of our salvation NOT being rooted in ourselves that points to the glory of God. Our salvation is not of ourselves, it is by grace; faith is the vehicle that God has chosen.
It is not of works. We are chosen.