Salvation is through Jesus submission to the Father, paying the price of our sin with His own death. Jesus and the Father have made very exclusive claims as these Scriptures show. If God is the almighty, all knowing, omniscient and only triune God, then those claims make perfect sense. They are simply a statement of fact.

John 3:14 And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up:
John 3:15 That whosoever believeth in him should not perish, but have eternal life.
John 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
John 3:17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
John 3:18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.
John 3:19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil.
John 3:20 For every one that doeth evil hateth the light, neither cometh to the light, lest his deeds should be reproved.
John 3:21 But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought in God.

John 3:36 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.

John 14:6 Jesus saith to him, I am the way, the truth, and the life: no man cometh to the Father, but by me.

Act 4:10 Be it known to you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom ye crucified, whom God raised from the dead, even by him doth this man stand here before you whole.
Act 4:11 This is the stone which was set at naught of you builders, which is become the head of the corner.
Act 4:12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.

When a people come to God, it is the Father who draws them.He shines His light on them.At first, most people reject the light.Over time, through His love which He is, the Father draws those who will be drawn.He keeps drawing them until the day when they accept Christ as the One who will rule over their lives and deliver them from the emptiness and pain of sin.Then, their most inner being, their spirit, is joined to the Spirit of Christ.That is the new birth. However, the fleshly nature still has no good in it. The battle between the flesh and the spirit begins. Before this point, the person was totally Satan's own, lost, free from God and slave to Satan, living in self-righteousness.

Heb 2:15 And deliver them who through fear of death were all their lifetime subject to bondage.

Heb 9:11 But Christ being come a high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building;
Heb 9:12 Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us.
Heb 9:13 For if the blood of bulls and of goats, and the ashes of a heifer sprinkling the unclean, sanctifieth to the purifying of the flesh:
Heb 9:14 How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
Heb 9:15 And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance.
Heb 9:16 For where a testament is, there must also of necessity be the death of the testator.
Heb 9:17 For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth.

Col 1:10 That ye might walk worthy of the Lord to all pleasing, being fruitful in every good work, and increasing in the knowledge of God;
Col 1:11 Strengthened with all might, according to his glorious power, to all patience and longsuffering with joyfulness;
Col 1:12 Giving thanks to the Father, which hath made us meet to be partakers of the inheritance of the saints in light:
Col 1:13 Who hath delivered us from the power of darkness, and hath translated us into the kingdom of his dear Son:
Col 1:14 In whom we have redemption through his blood, even the forgiveness of sins:
Col 1:15 Who is the image of the invisible God, the firstborn of every creature:
Col 1:16 For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him:
Col 1:17 And he is before all things, and by him all things consist.
Col 1:18 And he is the head of the body, the church: who is the beginning, the firstborn from the dead; that in all things he might have the preeminence.
Col 1:19 For it pleased the Father that in him should all fullness dwell;
Col 1:20 And, having made peace through the blood of his cross, by him to reconcile all things to himself; by him, I say, whether they be things in earth, or things in heaven.
Col 1:21 And you, that were sometime alienated and enemies in your mind by wicked works, yet now hath he reconciled