If God were not a Trinity, we could not be saved.  The reason is simple.  Our sins are against infinite and holy God; and we are, therefore worthy of infinite punishment.  Sins are related to the one offended.  If I slap a friend, he might get upset.  If I slap the President of the United States, the Secret Service would be all over me; and I’d be in jail.  The exact same action gets two totally different results because of whom the action is against.  Likewise, when we sin, we sin against the Holy King of the entire universe; and the penalty is eternal damnation.

There is no way that mere humans can satisfy the infinite judgment of a holy God because we are finite and sinners.  We are not capable of doing enough good or being good enough to make things right.  The only one left who is capable of performing a perfect act of atonement is God himself.  Therefore, God the Son came down in the form of Jesus and bore the wrath of God the Father.  But this could not be possible if God were not a Trinity: Father, Son, and Holy Spirit.  The second person of the Trinity became a man (John 1:1, 14; Phil. 2:5-8) and was subject to the Law (Gal. 4:4), bore our sins in his body on the cross (1 Pet. 2:24), and took our punishment (Isaiah 53:4-6).  Without God being a Trinity this could not be possible; and there could be no full and complete incarnation which would make the sacrifice of Jesus of infinite value, which in turn would satisfy the judgment of an infinite God.