The problem I see is that, according to scripture, non-believers do not seek after God. Faith comes to us through hearing, and hearing by the word of God. And as Christians the only way we can receive greater faith (IMHO) is to understand and seek out God through His word. We're not nearly as diligent about this as we should be (including myself).
My apologies. Here I am talking about the word of God and yet fail to post references. I would post the scriptural references but I'm having a bit of a problem with the Internet at the moment.
Romans 10:17
So then faith cometh by hearing, and hearing by the word of God.
Romans 3
10As it is written, There is none righteous, no, not one:
11There is none that understandeth, there is none that seeketh after God.
12They are all gone out of the way, they are together become unprofitable; there is none that doeth good, no, not one.
13Their throat is an open sepulchre; with their tongues they have used deceit; the poison of asps is under their lips:
14Whose mouth is full of cursing and bitterness:
15Their feet are swift to shed blood:
16Destruction and misery are in their ways:
17And the way of peace have they not known:
18There is no fear of God before their eyes.
19Now we know that what things soever the law saith, it saith to them who are under the law: that every mouth may be stopped, and all the world may become guilty before God.
20Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin.
21But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
22Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:
23For all have sinned, and come short of the glory of God;
24Being justified freely by his grace through the redemption that is in Christ Jesus:
25Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God;
26To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus.
27Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith.
28Therefore we conclude that a man is justified by faith without the deeds of the law.
Yes. Generally they don't, although in the Epiphany episode the pagan astrologers did just that. Another reason why Romans 3 should not be taken as bearing no exception.