Mind your own position and perspective in this thought experiment.
Like where are you in relation to that god? Are you an external observer who treats their actions as a black box being only aware of the inputs and outputs or are you within the god box, having complete awareness of their ideas and thought processes?
Because you seem to start from an outsiders perspective and try to justify an insiders perspective that doesn't necessarily follows from that.
The thing is, it's quite possible, maybe even necessary that from an outsiders perspective the actions of the god seem random. Like there's a good chance that this "randomness" is the origin story of the concept of a will in the first place.
So for example picture an inanimate object that is just described by the external forces pushing and pulling upon it and now compare it to idk an animal, which might act the same way under different circumstances or different under the same circumstances. So in other words it's not just the circumstances that motivate it's actions, but there's something inside it which follows it's own plan. There seems to be a will, that is independent or only loosely dependent on the particular situation.
So idk picture yourself looking at a 3-D model of the world where you've frozen time so that you can move around and observe things. Now, in that scenario, picture a compressed spring. It looks like an inanimate object, lacks most of the hydraulic parts common in life or whatnot. Still if you press "play" on your simulation and let time run again, it will decompress and return to it's "normal" shape.
So despite giving the initial appearance of randomness, it's nonetheless deterministic and the assumption of a will is more or less the result of different time scales and misunderstandings of cause and effect.
Now free will implies that your subject isn't just a system of compressed springs that react to inputs in a delayed, but nonetheless deterministic, way. But that it's actions are chosen by itself and are NOT causally determined by external conditions.
So regardless of whether the actions of the subject are predictable or random (to you!) they follow it's own motivation (thus not actually random to the agent), rather than whatever deterministic reason you model them with.
In other words they might as well be determined by initial states of the subject, but those initial states are NOT causally determined by the external state. So the agent acts because it WANTS to act like that.
While in a libertarian free will the agent is also free to want what they want. Again whether that looks to an observer to be random or orderly (both are aesthetic choices that someone could want...), the important part is that it's determined by the agent itself, instead of the agent being just a more complex inanimate object that who's state is the result of external forces.
The problem is that this creates this mind-body-problem, where "the mind", "the you", "the conscious self" or however you want to call it, is both intimately tied to the body with whom it interacts with the entire rest of the world both in terms of perception and action, so much so that it apparently can't exist without it. But with which it is at the same time it is not synonymous and from which it is actually causally independent.
So idk picture something like the system "excavator + operator". Where the excavator is the body and the operator is the mind. The operator in a sound proof cabin can only interact with the world via the excavator, but what they do is not determined by what the excavator experiences but what the operator wants.
Or picture an avatar in a computer game, where the person on screen is the body but the mind is actually outside of the "physical reality" that the avatar is in.
Now the nature of the universe (simulation) can force the avatar on a set deterministic path, but that doesn't actually control how the player feels about that and what they want or instruct their avatar to do.
So for example you could play a racing game, but instead of running around in circles you can crash the cars or run off cliffs and test the physics of the game. To an outside observer it may appear random, but with regards to your own motivation it makes perfect sense and might aim to be deterministic, meaning you actually react to inputs in a way that you think fits.
Though trying to fit expected outputs, is different than having your outputs be involuntarily defined by the inputs itself.
So no the inner workings of your god don't have to be random to produce results that are seemingly random. And they don't even have to seem random at all to begin with. They just need to be the result of the wants of the god and not determined by the inputs to it.
How that is supposed to know? No idea and the deeper we look into the human body the more and more options for a hiding place of the mind become obsolete. Though if it's like the avatar and the player we'd also never be able to find the player within the source code of our character either. And the very quest to find it there seems futile because there would be a necessary transition to a non-deterministic realm somewhere where our deterministic methods would struggle to find results. Or you know our models could be true and this free will simply doesn't exist and it's just an emergent phenomena of complex systems that is ultimately an illusion that we make up to make sense of the things that we don't understand, because we haven't found a deterministic cause and effect relation for them (yet).