The answer to that question likely relies on answers to questions that we don't have and likely never will have and in some regards we might even run out of even the concepts of what that means.
Like what is something that has no beginning? Everything that we can think of has a beginning. There are things that have begun so far in the past that we might have forgotten or never known it's beginnings and some things will last for so long that for the sake of a human life or even the life of humanity as a whole, they are "eternal", but what does it truly mean to have no beginning?
Because if you want to deduce something from that it's insufficient to think of something far back in time, but there truly must not have been a beginning.
Now there are some concepts without a beginning or end like for example a ring or circle. so if you stick to it's surface you can walk in either direction and you never find a place that looks like an origin and neither one that looks like an end. That being said the loop has been created and if you change your perspective and dare to leave the surface it has a beginning and an end. Even your move on the surface has a beginning and an end (the moment you touched it and the moment you stop doing so).
Even if you take the concept from the Neverending Story where a universe can have existed for billions of years despite the fact that you imagined it to exist just seconds ago, has a beginning, in fact it might have more than one, the moment it started "in Universe" and the moment the universe was created by thinking about it. Even if we say that "in universe" the universe had no origin, that is just something that we say but do we truly know what that means and what the consequences of that would be for that universe or is that just something that we ignore because we shift the narrative focus elsewhere?
So if we can't imagine what an unbounded universe would look like and how it came into existence how could we determine the consequences of that?
Also you can imagine toy examples of an infinite universe like ikd a tile pattern that repeats without end, which would be an example of a predictable or even predetermined universe. At the same time you could imagine more complex fractal structures or irrational numbers like π. It's infinite and yet never repeating so if i were to start at the xth spot of π and then progress from there would it be indeterministic because there's no pattern behind these numbers and little to work with in order to let you predict the next number or is it actually deterministic even predeterministic because the numbers in π are not actually random but you're following a sequence that had been known since the start of that thought experiment and that you could know if you leave the "in universe" point of view and make experiments with cycles and figure out the places of π and compare them to the sequence that you're given.
So even if you take something that has no end (is infinite) and forget that you started somewhere it could still be random or predetermined or be one and appear to be the other.
Likewise "god", "free will" and "the universe" are things that need careful definition. Because the idea of a universe implies that we all live in the same shared reality, while the idea of a god is of someone or something that is "supernatural" and that can bend and break the rules of reality, so to say something that is "outside" or "above"(=super) the reality. Which in turn is in conflict with the universe. Likewise if you define free will as something that is not tied to reality but that is truly free and can be a cause of itself, then that as well is a contradiction to the idea of a shared deterministic universe and would make you a god in itself.
Or you could live in a universe of gods, but then all that this means is that there are no gods and that you just got the rules of reality wrong.
So as these word can intersect, contradict, coexist or whatever else, it's very necessary to give a strict definition of these in order to be able to answer the question and in most cases we simply know to little to do so.
Also there are different versions of a god. Like you could have a magic superwizard that is omnipresent, omniscient and allpowerful, but if you're only interested in the act of creation then "god" might be your lazy roommate who left food to rot in the fridge and thus "created" an entire universe for the bacteria atop of it. Which also creates different perspective of creation. Like is creation the assembly of parts? Is it the creation of parts? Is it the set up of the environment? Or is it the act of pushing the start button? Is it all or none of these?
Also does free will exist in the first place and how could free will, even the concept of it exist in a deterministic world?
Like suppose you're playing a computer game, then "the world" is created by some kind of "god" (game designer) but also it's created by you through your interaction with it because otherwise it's just a bunch of 1s and 0s and flickering light, it's really you that creates it. And you are limited in your abilities but you have "free will" in terms of what you want to do. But to have free will requires you to already have free will to begin with. So you kinda have to answer the question as to whether free will exists before you'd even enter that scenario.
And even if the world had no beginning, you'd still have a beginning in this world and that would be the worlds beginning. So you would be the god who created that world despite it being someone else who put all the necessary parts into place.
TL;DR no you like can't deduce that because the existence of a starting point does not necessitate a predetermined universe... but that's still an educated guess as long as we still don't know all the answers, which we likely never will.
