Believing, or "faithing" to use your coined word, is given to sinners by God (but not forced upon them):Faithing or pisteuo in the Greek used 248 times in the NT, is the one thing He will not force upon us. He can do everything else for us, but we gotta faithe. He could provide redemption, and covering for our sins. He could provide direction, He can create mansions, pour out His spirit on us, but without faith ( a personal surrender to Him and a life inspired by such surrender) it is impossible to please God.
And He doesn't faithe for us!
You wrongly understand pisteuo to be believing, but let's use that incorrect word with your understanding.
Your saying that God is believing for you, no effort or choice on your part to do so.
Ya, it's non biblical, and ridiculous.
(Php 1:29 KJV) For unto you it is given in the behalf of Christ, not only to believe on him, but also to suffer for his sake;
I don't know New Testament Greek, but I understand from concordances that having faith and believing are the same thing. For example, the Greek word "pistis" is often translated into English as "faith". For example:
(Mar 11:22 KJV) And Jesus answering saith unto them, Have faith in God.
But sometimes it is translated as "believe" or "belief":
(Rom 3:26 KJV) To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus.
(Heb 10:39 KJV) But we are not of them who draw back unto perdition; but of them that believe to the saving of the soul.
(2Th 2:13) But we are bound to give thanks alway to God for you, brethren beloved of the Lord, because God hath from the beginning chosen you to salvation through sanctification of the Spirit and belief of the truth.
A closely related Greek word, "pisteuo", is usually translated into English as "believe". For example:
(Mat 24:23 KJV) Then if any man shall say unto you, Lo, here is Christ, or there; believe it not.
Greek has a verb form of "pistis", (which is usually translated as "faith", but sometimes "believe" or "belief"), and that verb form is "pisteuo." The English noun "faith" doesn't have a verb form.
Perhaps somebody with a knowledge of New Testament Greek can tell us whether "believe" is indeed (as you claim) a mistranslation. I don't think it is, but I repeat, I don't know Greek.