Romans 6:23 says that the gift of God is eternal life. If you want to think that eternal life only means living forever, I suppose that’s a verse you could pull out for support. However, read the verse carefully:
For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.
The life you and I have received through the gift of God is the life that is “in” Jesus. I take that to mean it is His life. Galatians 2:20 and Colossians 3:4 tell us that the life in us is His:
I have been crucified with Christ; it is no longer I who live, but Christ lives in me; and the life which I now live in the flesh I live by faith in the Son of God, who loved me and gave Himself for me. Galatians 2:20
When Christ who is our life appears, then you also will appear with Him in glory. Colossians 3:4
It is Jesus who is alive in me and Christ is my life. My eternal life! I have no life apart from Him and in Him I have His life.
So, when I came to Jesus, simply to receive what He offered me, I received His life. I received Him. Because He is eternal, the life in me is eternal.
But, what does it mean that He is eternal?