I'm glad you brought this up. The so-called existential Thomists are strong on this point. Frederick Wilhelmsen's "The Paradoxical Structure of Existence" [0] was my first encounter with this understanding of God. I strongly recommend this book for those whose interest was piqued by God-as-verb (in place of the God-as-teapot canard). The book offers a great interpretation of Parmenides and Heraclitus as having been closer to one another than the way in which they are typically presented in philosophical texts. For example, Parmenides correctly intuited Be-ing but failed as soon as he attempted to conceptualize and crystalize it into a noun (and also accounts for this curious silence on the plurality of beings in this regard). It is only then that he and Heraclitus part ways. The book continues with Avicenna's discovery of existence as something distinct from essence, then onto Averroes' error of demoting existence to the accidental order (understandable once to understand that the epistemic order is the reverse of the metaphysical order). Ultimately, we come to the understanding of God as the very act of existence, an act that precedes the essential order of things and cannot itself be conceptualized because it is not a thing, but precedes all things and causes them to be at every instant. That is a far more satisfying account of God than the caricaturish and anemic view of some ghastly thing floating about the universe performing magic tricks. It also makes God impossible to ignore as an unnecessary being-among-many.
Another book that touches on this subject is Etienne Gilson's "God and Philosophy"[1]. One of the most interesting bits for me is where he draws attention to the Old Testament where God reveals himself to Moses as "I am He who is". I always thought that was a rather curiously mysterious way of revealing oneself. But on this understanding of God as the act of existence, it makes perfect sense. God is, or God is Is, so to speak. So really, we trace this understanding of God -- albeit not a philosophical one -- to at least the second millenium BC.
Another book that touches on this subject is Etienne Gilson's "God and Philosophy"[1]. One of the most interesting bits for me is where he draws attention to the Old Testament where God reveals himself to Moses as "I am He who is". I always thought that was a rather curiously mysterious way of revealing oneself. But on this understanding of God as the act of existence, it makes perfect sense. God is, or God is Is, so to speak. So really, we trace this understanding of God -- albeit not a philosophical one -- to at least the second millenium BC.
[0] https://www.taylorfrancis.com/books/9781351477703 [1] https://yalebooks.yale.edu/book/9780300092998/god-and-philos...