My understanding is that determinism can be metaphorically described as "all events are set in stone". Therefore, choosing is set in stone, just like every other event. We cannot say that "choosing does not happen due to being set in stone". Quite the opposite. Choosing MUST happen if it is set in stone. We confirm this fact by noting people making choices, such as in the restaurant.
It is set in stone that we will enter the restaurant, sit at a table, read the menu, consider our tastes and dietary goals, and decide what we will order. One brick after the next. One stepping stone and then another.
Our walking, our sitting, our reading, our considering, and our choosing, were all equally "set in stone". And they all actually happened in physical reality.
So, the claim that an inevitable choice is not a choice simply does not hold up.
We are discussing it because you are insisting that it's correct and then saying that our ignorance that most of the options are not choosable somehow renders them choosable, we just won't choose them.
When we open the menu there will be multiple items that have a non-zero probability of being chosen. It will be set in stone from any prior point in time that this will be the case at the point of opening the menu. (Just like it was set in stone that at the beginning of the horse race, every horse had a non-zero probability of winning).
There is no item on the menu that is EVER "not choosable" at any point in time: past, present, or future. It was choosable yesterday. It is choosable now. And it will still be choosable tomorrow. It will only cease to be choosable when they take it off the menu.
We can prove that by simply ordering everything on the menu, assuming we can afford it all. And, it may take the restaurant time to prepare everything, but they will do so, and we will have our proof that every item can be chosen with 100% probability.
If our choice is set in stone and it only had one possible outcome, then there was never a choice to begin with.
"Set in stone" is a metaphor for deterministic causation. It is a "figure of speech", which, of course, cannot be taken literally. Like any other figurative statement, it is literally false. No one has laid down the future in actual concrete.
The claim that "there was never a choice to begin with" is similar. Because new events will always be reliably caused by prior events, every event will be causally necessary from any prior point in time. This means that our choices, like all events, will also be causally necessary.
We may say to ourselves, "It is AS IF there was no choice at all", or "It is AS IF only one item on the menu was choosable", or "It is AS IF the choice was made for me before I was born". Those are all figurative statements, and, like every other figurative statement, they are each literally false. We literally made a choice from a literal menu of literally choosable options. And our choice was literally made right then and there, and not one minute prior to that.
So, "there was never a choice to begin with" is literally false, in the same way that "set in stone" is literally false.