Matthew 7:21, . . . but he that doeth the will of my Father which is in heaven.
1 John 5:1, Whosoever believeth that Jesus is the Christ is born of God: . . .
Matthew 7
21 Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.
22 Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works?
23 And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.
I would view this as evidentiary, rather than conditional. The point is that believers do His will.
The same is true of 1 John 5:1.
1 John 5
1 Whosoever believeth that Jesus is the Christ is born of God: and every one that loveth him that begat loveth him also that is begotten of him.
2 By this we know that we love the children of God, when we love God, and keep his commandments.
3 For this is the love of God, that we keep his commandments: and his commandments are not grievous.
4 For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith.
5 Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?
Those who are born again overcome the world, as opposed to born again because they overcome the world. The means of overcoming is faith, and faith cometh by the hearing of the Word.
Belief in Christ is an impossibility for the natural man, and requires the enlightening ministry of the Comforter, thus we attribute the process of salvation wholly to God. Apart from His intervention there is no salvation. One must first be told of the Son of God before belief is possible. When God enlightens the heart there is no controversy—the unbeliever cannot argue with God. An example might be like this: we don't have to have someone tell us it is daytime when we stand out under the sun. It is truth that goes without saying. The unbeliever knows they are a sinner, they know Christ is righteous and they are not, they know they are headed for eternal judgment, and participates in this way: they do not reject that truth.
God bless.