Only God could pay the infinite penalty His justice demands for sin. But that would not be just, because “God is not a man...” (Numbers:23:19). The incarnation is therefore essential—but impossible if God were a singular being. “The Father sent the Son to be the Saviour of the world” (1 John:4:14). It was Jesus who died on the cross, not the Father nor the Holy Spirit.
Neither could a mere man, being finite, pay that infinite penalty. All through the Old Testament, Yahweh declares that He is the only Savior (Isaiah:43:3, 11; 45:15, 21; 49:26; Hosea:13:4, etc.). Thus Jesus had to be Yahweh but also a man. When God the Son became a man, He did not and could not cease to be God. Jesus was both God and man.
How could God become a man? Again, that is only possible through the Trinity. The Father didn’t become man, nor did the Holy Spirit. Even though we cannot understand this, we know it must be so. The penalty for our sins is infinite because God and His justice are infinite. Consequently, those who reject Christ’s payment on their behalf will be separated from God forever.