Buridan's ass states a problem where a hypothetical donkey has to decide between two equal choices (food and water, an equal distance apart from the donkey). Since they are completely equal, neither is chosen and the donkey dies. This may be solved by randomness, but God is not random. Would this create a problem for God (God cannot choose either one), given that such situations where two equal choices can exist for him?
These questions about applying logical paradoxes to God appear in this SE very frequently and they always amaze me. Why do people assume that God is subject to reason?
And in particular why do people who do not believe in God believe that that God in which they do not believe must be subject to reason?
And it makes no difference if the person contemplating is a student or a renowned philosopher.
The answer is quite simple. Imagine a God that transcends reason and now your question becomes nonsensical.
Here is Maimonides on the transcendence of God:
all people, both of past and present generations, declared that God cannot be the object of human comprehension, that none but Himself comprehends what He is, and that our knowledge consists in knowing that we are unable truly to comprehend Him. — Guide for the Perplexed, I 59:2
And as Osho put it in The Discipline of Transcendence Volume 2:
all great religious assertions are paradoxical. They may be in the Vedas, in the Upanishads, in the Koran, in the Bible, in the Tao Te Ching. Wherever, whenever you will find truth, you will find it paradoxical - because the truth has to be total; totality is paradoxical.
A doctrine is never paradoxical, a doctrine is tremendously consistent - because a doctrine is not worried about reality. A doctrine is worried about being consistent. It knows no reality. It is a mind game, and the mind is very, very logical. And the mind says don’t allow any contradiction in it.
Everything God-made is contradictory. That’s why people go on arguing about God.
And if you don't like to have it from Osho, then take it from Chomsky who argues that existence is mysterious in the sense that it transcends our capacity of understanding: https://www.youtube.com/watch?v=l-E0IEyS4qw
Yes, this would create a problem for God under certain assumptions about the nature of God. I.e. that God always acts on sufficient reason, and never chooses arbitrarily (=by a sheer act of will), not even in an equilibium, in a Buridan's-Ass-like situation.
Such a view was held e.g. by Spinoza. Here concerning free will:
It may be objected, if man does not act from free will, what will happen if the incentives to action are equally balanced, as in the case of Buridan's ass? Will he perish of hunger and thirst?..
...I am quite ready to admit, that a man placed in the equilibrium described (namely, as perceiving nothing but hunger and thirst, a certain food and a certain drink, each equally distant from him) would die of hunger and thirst. (Ethics 2/49)
And by Leibniz. Here concerning God:
Now, as in the Ideas of God there is an infinite number of possible universes, and as only one of them can be actual, there must be a sufficient reason for the choice of God, which leads Him to decide upon one rather than another. (Monadology 53)
That is, that the actual universe must be strictly better than any other possible universe. There cannot be two equally good possible universes, because if there were, God would not be able to choose between them.