The source of the hope:
As for you, you were dead in your transgressions and sins, in which you used to live when you followed the ways of this world and of the ruler of the kingdom of the air, the spirit who is now at work in those who are disobedient. All of us also lived among them at one time, gratifying the cravings of our flesh and following its desires and thoughts. Like the rest, we were by nature deserving of wrath. But because of his great love for us, God, who is rich in mercy, made us alive with Christ even when we were dead in transgressions—it is by grace you have been saved.
Ephesians 2:1-5
The living hope comes by the new birth.
Jesus replied, “Very truly I tell you, no one can see the kingdom of God unless they are born again.” “How can someone be born when they are old?” Nicodemus asked. “Surely they cannot enter a second time into their mother’s womb to be born!” Jesus answered, “Very truly I tell you, no one can enter the kingdom of God unless they are born of water and the Spirit. Flesh gives birth to flesh, but the Spirit gives birth to spirit. You should not be surprised at my saying, ‘You must be born again.’
John 3:3-7
For you have been born again, not of perishable seed, but of imperishable, through the living and enduring word of God.
1 Peter 1:23
The living hope comes by the resurrection of Jesus Christ from the dead.
If you declare with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved.
Romans 10:9-10
I pray that the eyes of your heart may be enlightened in order that you may know the hope to which he has called you, the riches of his glorious inheritance in his holy people, and his incomparably great power for us who believe. That power is the same as the mighty strength he exerted when he raised Christ from the dead and seated him at his right hand in the heavenly realms.
Ephesians 1:18-20