What does the Bible mean when it says God is invisible?

Scripture means that the Godhead—the Trinity, the Old Testament Elohim—is invisible Spirit. Out of that invisible Trinity, one person, God the Son, took on flesh and became visible. Thus Jesus is the image, or visible appearance, of the invisible God, not one of mankind's imagined gods.

Les teaches that the pronoun “who” in verse 15 refers to the Son, whose blood was given for redemption and forgiveness. Paul calls Him “the image of the invisible God.” God in His essence is invisible; the Trinity, the Elohim of the Old Testament, is that invisible Godhead, Spirit. But one person of the Godhead stepped out, took on flesh, and became visible. So God the Son, Lord Jesus, is the image or visible appearance of the invisible God. He is also the firstborn of every creature, meaning He is before anything else ever was. By Him, God the Son, all things were created in heaven and earth, visible and invisible, including thrones, dominions, principalities, and powers. Everything was created by Him and for Him. Les warns against bringing this person of the Godhead down to the level of the various other gods of mankind’s dreaming; that is blasphemy. He is the Creator, and one day every human being will know Him—the lost will meet Him at the great white throne and will not argue.

Colossians 1:15

Who is the image of the invisible God, the firstborn of every creature:

How does the Bible describe the Trinity and Elohim in relation to God's invisibility?

The Bible presents the Trinity, the Old Testament Elohim, as the invisible Godhead or Spirit. Out of that invisible Trinity, one person of the Godhead—God the Son—took on flesh and became visible in Jesus Christ. He is the image and visible appearance of the invisible God, the Creator of all things.