Hello Ogom, the WCF was speaking specifically of a true believer NOT being utterly destitute of the BLESSINGS of God (even if a believer has fallen into sin, wounded his conscience and grieved the HS, such that God withdraws the light of His countenance from him and, for a time, allows him to walk in darkness). No one (neither believer nor reprobate), at least on this side of the grave, is utterly destitute of God Himself.
For example,
Matthew 5
45 God causes His sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous.
It's also true that we have free will, and that if anyone "wants" to call out to Him they can (and as you pointed out, they often do .. as they say, there are no atheists in foxholes ). The problem for non-believers is that they are always interested in the benefits/blessings that God has to offer them, they just don't want Him, or the new life that He offers them in Christ (because that would mean giving up their sinful/worldly ways).
The other problem is free will. As I said above, non-believers want all of God's benefits/blessings, of course, but they have no desire to repent of their sin and surrender the reins of their lives to Him, so becoming a Christian (for them) would mean choosing to do so in direct OPPOSITION to their free will.
God bless you!
~Deut
p.s. - here is some Scripture to consider as well (about coming to God for salvation).
John 6
44 “No one can come to Me unless the Father who sent Me draws him; and I will raise him up on the last day.”
65 And He was saying, “For this reason I have said to you, that no one can come to Me unless it has been granted him from the Father.”
Romans 3
9 We have already charged that both Jews and Greeks are all under sin;
10 as it is written,
“THERE IS NONE RIGHTEOUS, NOT EVEN ONE;
11 THERE IS NONE WHO UNDERSTANDS,
THERE IS NONE WHO SEEKS FOR GOD.”