Amen.
Hearing and believing are the conditions for receiving eternal life.
Just as true are these words from the context, of John 5:24
24 “Most assuredly, I say to you, he who hears My word and believes in Him who sent Me has everlasting life, and shall not come into judgment, but has passed from death into life. 25 Most assuredly, I say to you, the hour is coming, and now is, when the dead will hear the voice of the Son of God; and those who hear will live. 26 For as the Father has life in Himself, so He has granted the Son to have life in Himself, 27 and has given Him authority to execute judgment also, because He is the Son of Man. 28 Do not marvel at this; for the hour is coming in which all who are in the graves will hear His voice 29 and come forth—those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of condemnation. John 5:24-29
...all who are in the graves will hear His voice and come forth—those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of condemnation.
- those who have done good, to the resurrection of life,
- those who have done evil, to the resurrection of condemnation
What you seem to be forgetting, is what believe means to the Lord.
Your trying to take a modern day meaning, and apply it to the first century words of Jesus.
Believing means more than "realize He exist's".
James deals with this subject.
You believe that there is one God. You do well. Even the demons believe—and tremble! James 2:19
Believe = Trust, commit, and obey.
Unbelief = Disobedience.
God, who “will render to each one according to his deeds”: eternal life to those who by patient continuance in doing good seek for glory, honor, and immortality; but to those who are self-seeking and
do not obey the truth, but obey unrighteousness—indignation and wrath, Romans 2:6-8
JLB