The Evolution of God by Robert Wright provides a naturalistic explanation for the idea of the existence of invisible beings.
http://www.evolutionofgod.net/excerpts_afterword/
By the Way, What Is God?
In this book I’ve used the word “god” in two senses. First, there are the gods that have populated human history—rain gods, war gods, creator gods, all-purpose gods (such as the Abrahamic god), and so on. These gods exist in people’s heads and, presumably, nowhere else.





A supernatural explanation: all of the polytheistic deities/ religions map to an ancient civilization.
it-1 p. 237 Babylon
Religion. Babylon was a most religious place. Evidence from excavations and from ancient texts points to the existence of more than 50 temples. The principal god of the imperial city was Marduk, called Merodach in the Bible. It has been suggested that Nimrod was deified as Marduk, but the opinions of scholars as to identifications of gods with specific humans vary. Triads of deities were also prominent in the Babylonian religion. One of these, made up of two gods and a goddess, was Sin (the moon-god), Shamash (the sun-god), and Ishtar; these were said to be the rulers of the zodiac. And still another triad was composed of the devils Labartu, Labasu, and Akhkhazu. Idolatry was everywhere in evidence. Babylon was indeed “a land of graven images,” filthy “dungy idols.”—Jer 50:1, 2, 38.
The Babylonians believed in the immortality of the human soul.—The Religion of Babylonia and Assyria, by M. Jastrow, Jr., 1898, p. 556.
The Babylonians developed astrology in an effort to discover man’s future in the stars. (See ASTROLOGERS.) Magic, sorcery, and astrology played a prominent part in their religion. (Isa 47:12, 13; Da 2:27; 4:7) Many heavenly bodies, for example, planets, were named after Babylonian gods. Divination continued to be a basic component of Babylonian religion in the days of Nebuchadnezzar, who used it to reach decisions.—Eze 21:20-22.
Israel’s Age-Old Enemy. The Bible makes many references to Babylon, beginning with the Genesis account of the original city of Babel. (Ge 10:10; 11:1-9)
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The numerous names for these deities in ancient Babylon represented spirit beings, but not from the true God's inner circle or anywhere else in his domain. Technically, the deities do exist and the names and idols demons (fallen angels) assigned to themselves when they initiated religion in Babylon through mediumistic rituals between these spirits and living people was to make their existence more tangible so people could worship them.
When the original language in Babylon was confused by God, Babylonians took their spiritistic practices with them and formed polytheistic religious cultures in various regions, some of which exist today. I believe in the supernatural explanation and in the spirit realm. Although spiritually I'm weak at this time, I've obtained tangible evidence for God. I've never gone in this direction, but tangible evidence for evil spirits is obtained through occult channels, ideally Black Magic (the Dark Arts).