Yep that's the truth!
He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
If you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved
And they said, Believe on the Lord Jesus Christ, and thou shalt be saved
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.
There's no such thing as predestination, we have freewill and a choice, to believe the gospel and believe in Jesus, or not. And once we believe we are to repent. If we don't believe and repent, then we are rejecting God and Christ. God doesn't save people before they believe, they must believe first to be saved!