Those who are born again are born again because God has purposed to save them- it is impossible that the purposes of God could be thwarted.
To be honest, however, I don't know that I agree that folks are often born again for years before they come to Christ.
I think there can be a period of spiritual incubation before the new birth where there is spiritual life growing but not yet a new birth- and that may indeed take years for whatever purposes God so chooses.
But it seems to me that Scripture teaches that once a person is born from above so that he can receive the things of the Spirit of God (namely the Gospel) that he does shortly thereafter- often times immediately.
Spiritual incubation? Wow, once you go off the tracks you just spin off into more error.
You do not have one verse to present that shows regeneration comes before faith. I and others have presented at least half a dozen verses that all show faith precedes life. Here is one for instance.
John 3:36 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
This verse says the person that believes has life, and the person who believes not shall not see life.
So, you cannot have life until you believe. You cannot be in some stage of incubation or development of life, until you believe you are
DEAD. There is no such thing as 25% dead (or alive) or 50% dead (or alive), until you believe you are
100% DEAD. You are either dead, or alive, there is nothing in between.
Again, Calvinism's problem is they don't understand what spiritual death is. They try to compare it to physical death. It is true that someone who is physically dead cannot function, but spritually dead people can. To be spiritually dead means to be separated from God in your sins, but it does not mean a person lacks ability.
The story of Cain shows this. We know Cain is lost, but God said he could do well and would be accepted. God does not accept evil, and so this proves the spiritually dead man can do some things acceptable with God.
That spiritual death speaks of judgment and not inability is shown by Jesus.
John 8:24 I said therefore unto you, that ye shall die in your sins: for if ye believe not that I am he, ye shall die in your sins.
A person cannot be partially alive as you try to say. Until they believe they are DEAD in their sins. You cannot be alive until your sins are forgiven, and you cannot have your sins forgiven until you believe.
And notice Jesus said "if" to these persons. There is no such thing as "if" in Calvinism. You are either elect and must believe, or unelect and cannot believe.
But Jesus said "if" to these unregenerate persons, showing that the unregenerate can believe.