Are there any denominations that give official advice on how to win atheists for Christ who are very strong in philosophy, logic and skepticism?

As Ken Graham says, you are probably going to find much more in specific ministries than official church programs.

Within Catholicism, the Word on Fire ministry has focused to a significant degree on intellectual atheists. You can see here

https://www.wordonfire.org/resources/browse/topic/atheism/

for some resources from them on this topic.

However, when you say "I see no possible way of evangelizing them through purely intellectual/argumentative means." I think this is right. Very rarely, an atheist might change to belief in God through entirely abstract argumentation, but at that point, they still lack the experiential reference points that, IMHO, are more important. You're not really fighting the intellectual beliefs. Yet, I think removing intellectual obstacles to an ongoing relationship with God is usually going to be important, either way.

I'll offer a brief supplemental argument from the perspective of The Church of Jesus Christ of Latter-day Saints.

From the record of the prophet Alma:

And now, as the preaching of the word had a great tendency to lead the people to do that which was just—yea, it had had more powerful effect upon the minds of the people than the sword, or anything else, which had happened unto them—therefore Alma thought it was expedient that they should try the virtue of the word of God. (Alma 31:5)

Nephi taught:

when a man speaketh by the power of the Holy Ghost the power of the Holy Ghost carrieth it unto the hearts of the children of men. (2 Nephi 33:1b)

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The wisdom of the world is a constantly changing picture. It can answer many questions, but in doing so has a funny way of creating at least as many new ones (e.g. because more is known about the universe today than 4,000 years ago, we are asking more unanswered questions about the universe today than people were 4,000 years ago).

Knowledge that the world gives, the world can take away. Knowledge that God gives is knowledge the world cannot touch.

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Conclusion

The word of God and the influence of the Holy Spirit can change hearts & minds (specifically open hearts & minds) in a way nothing else can.

Several Answers There are several answers to this question and lengthy introduction. (1) Seminaries First note that quite a few Denominations sponsor or support several Bible Colleges and Seminaries. Scholarly researchers usually congregate in the seminaries. AND is is the custom and habit for one or more of them to write and publish Systematic Theologies.

In most of these Systematic Theologies there is an opening section dealing with the Existence and Attributes of God. Quite a few give an expose of several of the "proofs of God's Existence." (Anthropological, Cosmological, Teleological, Historical, etc.) These books would be as close as one could come to obtaining OFFICIAL BELIEFS of any denomination. And any "evangelism" would be based on these truths. Seminarians would take courses on this type of philosophical and logical Apologetics, and incorporate it into their church which they would pastor. Evangelism in the local church would have a scholarly foundation.

• Louis Berkhof
• Augustus Strong
• Henry Thiessen
• Charles Hodge
• John Mueller
• Robert Dabney
• Thomas Aquinas
• Donald Macleod (?)

(2) Para-Church Orgs Some denominations are not capable of establishing A Seminary, or do not have seminary professors efficient in Evangelistic Apologetics. The local churches in these denominations are therefore reliant upon Para-church organizations for training their congregations on evangelizing atheist, agnostics, and skeptics. These organizations have highly skilled researchers, lecturers, disciplers, whom local churches can resort to for wisdom in reaching the unbelievers. A few of these are:

• Campus Crusade for Christ (Cru)
• Navigators
• Intervarsity
• Socrates in the City (Eric Metxas)
• Discovery Institute
• C.S. Lewis Society
• Institute for Creation Research
• Biologos

Denomination boards would examine and consider recommending one or more of these that are compatible with their denomination creeds. This would be surrogate OFFICIAL ADVICE, for which the OP asks.

Many of these organizations have lecturers and seminar speakers available for ministering in local churches. As well as literature, videos, a discipleship programs. Beyond this there is a plethora of web sites dealing with a philosophical, scholarly approach to evangelism, that denominational pastors could use as a resource.

John Lennox, Norman Geisler, Jason Lisle, Gary Parker, Jonathan Wells, Lee Strobel, Eric Metaxas, Petr Kreeft, William Lane Craig...are all knowledgeable scholars, who are able to give Official Advice on dialoging with unbelievers.

Unreasonable Resignation The middle paragraph of this OP presented an unreasonable resignation, throwing up his hands in defeat! It ignores the facts of the conversion of even the hardest of skeptics in history. And it displays an ignorance of the many ways unbelievers come to faith. And it is unaware of the purpose of "reasons, proofs, logical arguments, etc." (Most dialog is "pre-evangelism. Logical reasons dropped in the mind become tools for the Holy Spirit to work with.)

Most of the confrontation/gentle dialog with atheists and agnostics is

(a) pulling weeds (dealing with misinformation and disinformation about God),

(b) planting seeds (seeds of doubt concerning the inadequacies of the atheistic worldview,

(c) fulfilling needs (even atheists need friends and are human with many mortal-type needs; love can bring a mighty man to his knees),

(d) performing deeds (prophecies, see 1 Corinthians 14:24-25, healings 1 Cor. 2:4-5, Heb. 2:4, charity),

(e) explaining Creeds (many college atheists haven't a clue what Christianity is all about! Spiritually challenged they are! Also note how many biblical questions contestants on Jeopardy are unable to answer.)

The Holy Spirit is able to use many different tools to change the Minds and Wills of even the hardest skeptic. Scientists have come to faith by intellectually trying to resolve the "design" in the universe. Pondering the existential meaning of the universe has opened the minds of some. The logical bankruptcy of the Atheistic worldview has led others to consider Theism.

Paul and Areopagus In Acts 17:17 we see that the Apostle Paul was not hesitant to use metaphysical arguments in addressing the scholars of Athens. (cosmological, teleological, anthropological) He was so successful that "among a number of others," Dionysius, one of the scholars, became a convert! Men and women were convinced.

Note that when Paul referred to the "wisdom of men" in 1 Corinthians 1:21, he was referring to the philosophies of the Stoics, Epicurians, Pythagageans, and Platonic Athenians. He was NOT being adverse to Apologetics. The way a word is defined and used is determined by its context. So here "wisdom" was referring to the philosophies invented by men only.

But "wisdom," in reading the whole counsel of God, is a blessing and creation of God. In fact, most do not realize that wisdom was the very first thing created!

The Lord brought me forth as the first of His works, before His deeds of old; I was appointed from eternity, from the beginning before the world began. (Proverbs 8:22,23)

By wisdom the LORD laid the earth's foundations; by understanding, He set the heavens in place; by His knowledge the deeps were divided, and the clouds let drop the dew.

So God is not adverse to "wisdom" and its use by His disciples to convince unbelievers of the existence of God and their need to convert. Anyone who comes to salvation must believe He exists first. (Hebrews 11:6) Then they can live a life of faith that He will reward all those seek Him earnestly.

Apologetic reasonings are not the Gospel, but they lead men to the Author of the Gospel. Holy Spirit anointed Apologetics is the grease on the door of the closed mind so it will open easily when Christ comes knocking.

I do not have this as an official denominational teaching from either the Baptist church I started out in or the Foursquare Church I currently attend but the grassroots teaching and practical lifestyle are generally as follows with the Baptists leaning heavier on doctrine and reason while Foursquare lifts interpersonal relationship to higher relevance.

By and large a relationship with God through the Lord Jesus Christ is not initially accessed intellectually (Matthew 16:17). Appreciation of it can grow in the rational mind once the mind has begun to be renewed beginning at the new birth but very few (if any) can be reasoned into the kingdom. This is because the sin nature lies beneath and empowers the intellect. Until slavery to sin is broken the intellect has no other master.

That is not to say that reason should not be employed in defense or proclamation of the Gospel. When the Apostle Paul would enter a town he would go first to the synagogue and reason with the Jews from the Scriptures (and I daresay he might have swayed some) and when he was in Athens at the Areopogus, he reasoned with the philosophers and skeptics of his day according to their proclivities. What he also did, however, was to be very careful about how he lived among them so that, when his preaching was done, his message would not be disqualified by his way of life. I don't know if it is fair to say that one avenue carries more power than another.

Then, too, there were "ships passing in the night" opportunities where only a brief interaction was afforded. Only from God's perspective can the effect of such interactions be properly weighted. Behind, under, and over any evangelization effort lies the power of prayer as we minister the Gospel of the God who saves.

But when anything is exposed by the light, it becomes visible,  for anything that becomes visible is light. Therefore it says, “Awake, O sleeper, and arise from the dead, and Christ will shine on you.” Look carefully then how you walk, not as unwise but as wise, making the best use of the time, because the days are evil. Therefore do not be foolish, but understand what the will of the Lord is. - Ephesians 5:13-17