Jesus says whoever believes has eternal life. This is a passage that is normally understood in one of two ways. Most see it as a job offer leading to salvation. For whoever chooses to believe and accepts the terms. Some see it as an announcement aimed at those who believe as they hear, providing directions for holy living.
And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel. Mark 1:15 (KJV)
Obviously the gospel is aimed at unbelievers; they're told to repent and believe.
And he said unto them, Go ye into all the world, and preach the gospel to every creature. Mark 16:15 (KJV)
Every creature isn't a believer.
And when there had been much disputing, Peter rose up, and said unto them, Men
and brethren, ye know how that a good while ago God made choice among us, that the Gentiles by my mouth should hear the word of the gospel, and believe. Acts 15:7 (KJV)
Hearing the gospel comes first - then believing it.
... and how shall they believe in him of whom they have not heard? and how shall they hear without a preacher? 15 And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace ... Romans 10:14-15 (KJV)
The preacher preaches the gospel to unbelievers.
In whom ye also
trusted, after that ye heard the word of truth, the gospel of your salvation ... Eph 1:13 (KJV)
They heard the gospel and afterward believed it.
For unto us was the gospel preached, as well as unto them: but the word preached did not profit them, not being mixed with faith in them that heard
it. Heb 4:2 (KJV)
The gospel comes to unbelievers so that they may become believers.
Jesus says whoever believes has eternal life.
Yes He does - but that sounds like a summary statement. If you're attempting to discuss a chronological or a cause & effect relationship between faith and salvation, you'll need to post what particular chapter & verse it is that you're referring to.