No one can be saved unless God first calls him/her:
John 6
35Then Jesus declared, "I am the bread of life. He who comes to me will never go hungry, and he who believes in me will never be thirsty. 36But as I told you, you have seen me and still you do not believe. 37All that the Father gives me will come to me, and whoever comes to me I will never drive away. 38For I have come down from heaven not to do my will but to do the will of him who sent me. 39And this is the will of him who sent me, that I shall lose none of all that he has given me, but raise them up at the last day. 40For my Father's will is that everyone who looks to the Son and believes in him shall have eternal life, and I will raise him up at the last day."
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43"Stop grumbling among yourselves," Jesus answered. 44"No one can come to me unless the Father who sent me draws him, and I will raise him up at the last day. 45It is written in the Prophets: 'They will all be taught by God.' Everyone who listens to the Father and learns from him comes to me. 46No one has seen the Father except the one who is from God; only he has seen the Father. 47I tell you the truth, he who believes has everlasting life.
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61Aware that his disciples were grumbling about this, Jesus said to them, "Does this offend you? 62What if you see the Son of Man ascend to where he was before! 63The Spirit gives life; the flesh counts for nothing. The words I have spoken to you are spirit and they are life. 64Yet there are some of you who do not believe." For Jesus had known from the beginning which of them did not believe and who would betray him. 65He went on to say, "This is why I told you that no one can come to me unless the Father has enabled him."
No one seeks God on his/her own but only in response to God's call.
God "foreknew" who would and who would not respond favorably to His call, and based on that foreknowledge, He chose whom He would call:
Romans 8
28And we know that in all things God works for the good of those who love him, who have been called according to his purpose. 29For those God foreknew he also predestined to be conformed to the likeness of his Son, that he might be the firstborn among many brothers. 30And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified.
Ephesians 1
11In him we were also chosen, having been predestined according to the plan of him who works out everything in conformity with the purpose of his will,
Rest assured that if your desire is to be saved, then you will be saved. You wouldn't have that desire if God hadn't called you and enabled you. Those who are not chosen do not want to be.
The faith that you have - that is, believing in Jesus Christ and putting your trust in Him for salvation - is a gift given to you by God:
Ephesians 2
8For it is by grace you have been saved, through faithand this not from yourselves, it is the gift of God 9not by works, so that no one can boast. 10For we are God's workmanship, created in Christ Jesus to do good works, which God prepared in advance for us to do.
And God doesn't take back gifts He has given: "for God's gifts and his call are irrevocable." (Romans 11:29).
"...being confident of this, that he who began a good work in you will carry it on to completion until the day of Christ Jesus." (Philippians 1:6)