Are you saved because you believe? Or do you believe because you are saved?
By His grace He gives the gift of belief through faith to those who love Him.
Ephesians 2:8
For by grace you have been saved through faith. And this is not your own doing; it is the gift of God,
By His grace He gives the faith to believe.
That does not say that faith is a gift. It says that salvation, which is by God's grace through our faith, is the gift of God.
The fact that salvation is offered to all people is made abundantly clear in scripture.
John 3:16
For God so loved the world that
he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. 17 For
God did not send his Son into the world to condemn the world, but to save the world through him.
1 Timothy 2:3 This is good, and pleases
God our Savior, 4 who wants all people to be saved and to come to a knowledge of the truth. 5 For there is one God and one mediator between God and mankind, the man
Christ Jesus, 6 who gave himself as a ransom for all people. This has now been witnessed to at the proper time.
1 John 2:1 My dear children, I write this to you so that you will not sin. But if anybody does sin, we have an advocate with the Father—
Jesus Christ, the Righteous One. 2 He is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world.
Revelation 22:17 The Spirit and the bride say, “Come!” And let the one who hears say, “Come!” Let the one who is thirsty come; and
let the one who wishes take the free gift of the water of life.
The reason that some don't accept the gift is not because God hasn't given them the gift of faith, but rather is because they willingly choose not to accept it.
Matthew 22:1 Jesus spoke to them again in parables, saying: 2 “The kingdom of heaven is like a king who prepared a wedding banquet for his son. 3 He sent his servants to
those who had been invited to the banquet to tell them to come, but they
refused to come.
Matthew 23:37 “Jerusalem, Jerusalem, you who kill the prophets and stone those sent to you,
how often I have longed to gather your children together, as a hen gathers her chicks under her wings,
and you were not willing. 38 Look, your house is left to you desolate.