God didn't make a mistake ever. But He loves us more than people can imagine and He demonstrated that love on the cross.
Greater love hath no man than this, that a man lay down his life for his friends.
John 15:13
6 For when we were yet without strength, in due time Christ died for the ungodly.
7 For scarcely for a righteous man will one die: yet peradventure for a good man some would even dare to die.
8 But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.
Romans 5:6-8
9 In this was manifested the love of God toward us, because that God sent his only begotten Son into the world, that we might live through him.
10 Herein is love, not that we loved God, but that he loved us, and sent his Son to be the propitiation for our sins.
1 John 4:9-10
And walk in love, as Christ also hath loved us, and hath given himself for us an offering and a sacrifice to God for a sweetsmelling savour.
Ephesians 5:2
21 But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; 22 Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference: 23 For all have sinned, and come short of the glory of God; 24 Being justified freely by his grace through the redemption that is in Christ Jesus: 25 Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God; 26 To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus.
Romans 3:21-26