An objection I have heard three times now (that I recall) essentially is that "Isn't God an actual infinite?". My answer, perhaps to the surprise of some, is a hard no. But let me explain this in detail.
To be an actual infinity, you have to:
A. Be composed of an infinite number of "parts".
B. Take up an infinite amount of space.
C. Exist for an infinite amount of time.
In the case of A, God is not composed of "parts". Even the trinity is not best described as three parts of a whole, but rather as three persons within one essence. But even if it was, it still isn't an infinite number of parts.
On to B...God is outside of space entirely, and does not literally take up space (except in his incarnation as a human, Jesus of Nazareth). God is said to be everywhere, and fills his creation in some sense. But even taken as woodenly literal, this would only be an infinity if the universe itself were spatially infinite, which is highly unlikely and, in my opinion, logically impossible. So that takes care of that.
Now we get to C, the really controversial one. Does God exist for an infinite amount of time. Well, it depends on how you view God's relation to time. Obviously the Bible speaks to God's omnipresence and eternality. But there is more than one view on what being eternal really means. You could view eternal as existing for an infinite amount of time. Or you could take the alternate view, that actually makes more sense to me, and is more logically coherent.
God is outside of time. God is not limited by a time dimension of cause and effect as we are. As the ultimate cause, God does not experience time. As such, God is timeless, rather than time-infinite. Calling God infinite in time is like calling a Colorless piece of paper infinitely red because the color red does not apply to it.
Now, there is also the view that God "entered into time". At least with regard to Jesus' incarnation, I would agree. But in his "pure" state, God is outside of time. Hence, how God creates time in Genesis 1:1.
Some would also argue for God being an actual infinity from his omnipotence and omniscience. But I think this could be better described as "unlimited" rather than "infinite". God is not limited by anything, he can do all. But that doesn't mean his power is an actual infinity. Power is just potential, not actuality.
Thanks for reading!