Further, the "physical" universe is only a part of the whole. If you mean the matter based universe then it is easily the smaller part of the universe. Energy seems to make up more of the universe, and we are still learning about it in the greater whole. So, there is this issue that you have to consider the concept of gods outside of the "physical" realm as we know, but not in some magical realm, just one we don't have enough information on. It's still a part of physics.
You misunderstand me. By "physical universe" I mean everything in existence that can physically be observed, including all forms of matter and energy.
Now about physical gods, if you have a god that exists in our universe like we do then they may be constrained similiarly. But, being a part of our universe is not the same as having the same limitations that we as humans have. We have an incomplete understanding of what is going on around us so we don't even know whether or not we can overcome things that currently constrain us as humans.
I think the point here is that idea of a god with free will flat out contradicts what we know about how things work. That's not to say that a god does not exist, but rather that the very idea of a god with free will does not make sense. The idea of me having free will does not make sense either, and I'm ok with that even though it doesn't make sense.

Exactly. "Randomness" is a conceptual model
invented by the human mind in an effort to explain what we observe. We call a dice roll "random" because if we do it enough times we expect a certain distribution of outcomes. But the fact is, if you know everything about the initial state of the die and the forces acting it, you can calculate exactly how it will roll. "Randomness" is something humans use to account for the fact that we don't have all the information needed to predict with accuracy.
Science assumes at its most basic fundamental level that the universe works in this way. There is a direct cause-and-effect relationship between the previous and current state of any entity in existence. Therefore, the implication is if you know everything about the laws that govern the physical universe, and you know exactly where every entity was at any given time, you can calculate exactly how every particle will move for all of the past and future. Which would imply that everything, even a god who lives in the observable physical universe, is predetermined.
But a God who lives outside of our observable universe would not be subject to this constraint. He could change things without being affected by them.
Imagine it like you're playing the Sims, but you leave the mode on where your Sims do their own thing if you don't tell them what to do. If you never touch the keyboard or mouse, your Sims will go about their lives, subject solely to the constraints of their AI. Give the same state, they will do the same thing every time. (If their actions have some random element, their behavior might differ, but they are at the mercy of the random number generator. Given the same
seed, they will always do the same thing.) They act out their lives as if they have free will, but they are actually just following a specific set of instructions laid out in the game and AI code. In this analogy,
the game is the universe, the Sims are people, and the game code is the laws of physics. And the player is god. The player lives outside the game code, but can effect things within the game universe. He can pause the game and move things and people around. He can give people tasks to do. He can use cheats to improve the lives of the players. If he wants, he may even be able to hack the game and change the game code (laws of physics). Since he lives outside of the game code, he is not subject to the same equations that dictate how the Sims and the world will behave.
But the Sims cannot know about the player. All they know is what is inside the game code, because that is all they can possibly see or interact with. Anything outside the game is undetectable to them.
This is what I mean when I say that there are questions science cannot answer. Are we just "sims" in some god player's simulated universe? There's no way to know, because we don't have access to anything outside the universe we exist in.