I’ve always been uncomfortable with assertions that God is “infinite”. Infinity is a mental concept that is not directly applicable to anything concretely real. It is useful in mathematics, especially the concept of the infinitesimal in calculus. But it is improper to apply it as an adjective for anything that is real.
One can truly say: “It is not possible to set a limit to what God can do.” But this does not imply: “there is no limit to what God can do.” In mathematics, one can add and multiply the largest imaginable numbers, any number of times, and the result is still finite. The theological analog is that anything you can imagine God doing, He can do more. But it will still be finite.
God transcends space-time, but this transcendence should not be described as “infinity”. Transcendence of space-time is not the same thing as a limitless expansion of space-time. All of His actions within the creation are constrained by the finiteness of the creation. To the extent that He interacts with the world, He is finite. We can say that in His transcendence, He transcends finitude; and in His immanence, He partakes of finitude. But in neither case is the concept of infinity applicable.
Omniscience means He knows all things. But this is necessarily finite since the object of His knowledge, all things, is finite. Some people believe He also knows all possible future contingent counter-factuals, which may be construed as infinite. But I regard this “middle knowledge” hypothesis as highly speculative and misguided. Similarly, His omnipotence is finite, in that His power is exercised upon finite objects. And furthermore, His omnipresence has meaning only within the realm of space-time, which is finite. These “omnis” do not imply infinity.
Is anything lost by discarding the claim of infinity? I think not. The qualitative gap between God and the creation is preserved, in that He alone is non-contingent, and He alone transcends space-time. By shedding this element of irrationality, our testimony and our faith become more credible. So, I believe it is best to affirm only what scripture affirms, without adding to it. It is sufficient to say: “He is all-knowing and almighty, and there is no other like Him.”