God has looked down from heaven upon the sons of men
To see if there is anyone who understands,
Who seeks after God.
Every one of them has turned aside; together they have become corrupt;
There is no one who does good, not even one. Psalm 53:1b-3 NASB
Such is a biblical description of the depravity of mankind. How can a being so described ever be reconciled to God? Obviously, some kind of gracious intervention by God would be required, but what kind and to what degree?
Suffice it to say, the depraved person is enabled to respond to God with faith as God speaks to him or her. A rewiring of the person is not required at that point, just an interaction with God. When the Spirit of God interacts with a depraved person, that person is, in effect, freed from their natural state of depravity (i.e., their inability to know good and to know God) and given a window of opportunity to respond to God with faith.
This is the most natural reading of the biblical testimony of how mankind has been since the Fall. Whether we look at Adam and Eve, Noah, Abraham, Moses, Isaiah, or the Apostles, the pattern is the same--God spoke to them and they were able to respond. None of them is reported to have been regenerated in order for this to happen, no great re-fabrication of their humanity was ever mentioned; therefore, the implication is that it was not necessary. Only the logical necessity within an extra-biblical theological system (Calvinism) even remotely suggests such a thing, not the text of scripture.
What the scriptures do teach indirectly by example, and directly through the words of Christ is that depraved human beings have no way or means (or desire) to find God by their own self-initiated effort. Even if they could make such efforts unassisted, those efforts could never be effective, for God is not obligated to appear at the summons of a sinner. God is not like a set of misplaced car keys which are found if searched for thoroughly "whether they want to be or not." If he did not make himself findable, available, we would never encounter him.
The truth is, if he didn't draw and woo us by his Spirit, we would never look. And yet, our depravity is not of such a nature that it cannot be overcome by God showing up. His tap on our shoulder is sufficient to give us the power and reason to turn to him, without the necessity of reworking our inner being just in order to do so. The scriptures do not relate the latter occurring anecdotally nor describe such theologically. Embracing such a thought can only muddy the waters and make confusing what isn't.