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?
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.