Jonathan Edwards, John Wesley and other Great Awakening writers often use the expression "swallowed up in God". It also appears in the writings of Bernard of Clairvaux.
Does it have a scriptural or other early origin?
I believe you are looking for 2 Corinthians 5:4 "mortality might be swallowed up of life.", as further elaborated and interpreted by Irenaeus of Lyons, who said
For this corruptible must put on incorruption, and this mortal must put on immortality. So, when this mortal shall have put on immortality, then shall be brought to pass the saying which is written, Death is swallowed up in victory. O death, where is thy sting? O death, where is thy victory?” Now these words shall be appropriately said at the time when this mortal and corruptible flesh, which is subject to death, which also is pressed down by a certain dominion of death, rising up into life, shall put on incorruption... becomes immortal and incorruptible, not after its own proper substance, but after the mighty working of the Lord, who is able to invest the mortal with immortality, and the corruptible with incorruption. And therefore he says, “that mortality may be swallowed up of life. He who has perfected us for this very thing is God, who also has given unto us the earnest of the Spirit.” ... Now, what is mortal shall be swallowed up of life, when the flesh is dead no longer, but remains living and incorruptible Against Heresies 5.13
For by no other means could we have attained to incorruptibility and immortality, unless we had been united to incorruptibility and immortality. But how could we be joined to incorruptibility and immortality, unless, first, incorruptibility and immortality had become that which we also are, so that the corruptible might be swallowed up by incorruptibility, and the mortal by immortality, that we might receive the adoption of sons? Against Heresies 3.19
I realize this has a bit of a different cast than "swallowed up in God", but I think the line of thought is evident. Irenaeus actually comes closest to referring to being swallowed up in God in reference to Christ, saying "the human nature [of Christ] being swallowed up in it (the divine)" Against Heresies 3.19
I appear to have largely retraced your steps in looking for the phrase "swallowed up in God" itself in later texts, which appears in:
Similar thoughts, although not this phrase, are expressed in, eg. Angela of Foligno. (see McGinn, Bernard. "Lost in the Abyss: The Function of Abyss Language in Medieval Mysticism." Franciscan Studies 72.1 (2014): 433-452.)
The only reference I could find concerned Jonathan Edwards. Originating from The Biographical Dictionary of Evangelicals, I found the following site reference:
However, in 1721 he came to the conviction, one he called a "delightful conviction." He was meditating on 1 Timothy 1:17, and later remarked, "As I read the words, there came into my soul, and was as it were diffused through it, a sense of the glory of the Divine Being; a new sense, quite different from any thing I ever experienced before I thought with myself, how excellent a Being that was, and how happy I should be, if I might enjoy that God, and be rapt up to Him in heaven; and be as it were swallowed up in Him for ever!" (Biography - Jonathan Edwards)
The only Biblical reference I could find for God swallowing anything was Isaiah 25:8: "He will swallow up death forever. The Sovereign Lord will wipe away the tears from all faces; He will remove His people’s disgrace from all the earth. The Lord has spoken." (NIV)
I can only speculate that perhaps the idea of being swallowed up in God might come from several passages, such as Psalms 5:11, that speak of taking refuge in Him.