It is the Lord Himself who said believe in His Son so "believing" is meant to be a work of man but that is not what saves you nor does it produce faith in and of itself. God isn't believing on your behalf, He requires you to do it which is why He gave us volition to begin with.
Faith is the result of salvation, believing is something we must do, not only in regard to the Gospel but throughout our walk with the Lord. The power in His word is what transforms our believing into faith and why it must be tested to see if what we say "I believe" is indeed in the truth of the Word for only from the word can faith come.
One can only have as much faith as they have truth. You can say you believe something to the cows come home and you might be utterly dinkum about it, but if what you believe is not true or if you only think you believe it but testing shows you to be lacking, you will not have faith.
So you can believe one must be born again before they can believe, but if it is not true, you do not have faith and without faith, you cannot please God.