So, here's the rub. A creator with finite years in their own existence can create an eternal universe in which they do not ever not exist.
It starts with establishing a "time loop symmetry" at "the start".
Time has "a point where things changed" but no real "beginning". The creator was there for that.
Then at "the end", you have a similar structure: all the particles rip apart but ostensibly keep doing that in a way where the measure of number just loops back around meaninglessly forever.
The creator was there in that moment too, and in all moments hereafter.
Essentially, just populate each bound of time with a "spin lock".
A quote
from Elon Musk:
"...the games will become indistinguishable from reality. ...there would probably be billions of such computers and set-top boxes. ...it would seem to follow that the odds that we're in base reality (NOT a simulation) is one in billions"
There is also the
Roy game and Alan Watt's dream thought experiment.
The purpose could be for entertainment and personal growth. These simulations would mostly run forwards in time though often run faster than real time (like in the Roy and dream examples).
So I don't think they're compatible with your scenario of not having a beginning. Your scenario is possible but I think it is much more likely that it isn't the case assuming that there are billions of simulations. Those examples also do not involve an eternal universe. I think another problem with the kind of "block universe" you're proposing is that you've got to store data from every point in time which would involve huge amounts of memory.
"Having a beginning" is a function of context. "A beginning relative to what?"
Imagine a system where you can "look up an image at a time". Just one person, in an infinite field, with a box. I could simulate this fairly easily, and with a little bit of imaginative massaging, just ignore the fact that our environment is composed of 'memories' being processed particularly by a single processor, and not spacetime units being processed by field interactors.
I, being the quantum entity defined by x86 mechanics that I am in this simulation turn the pad to "the day before Last Thursday"
I see a Wednesday before last Thursday, in which my egg that I hatched from is almost ready to hatch.
I turn it back further, and I see the egg getting smaller.
I turn it all the way back to the Thursday Before Last, and now it's just a barren field.
I turn it back to the Wednesday before that, and now it's just a barren field. I turn it back further...
You guessed it, barren field.
I, from the outside, have looped the barren field state and have a mechanism that no matter how far back you turn that little screen of yours, you see a barren field.
But not only that every frame of that "barren field" at any point in time is subtly unique! There are clouds overhead, and when you rewind the time infinitely, the clouds still fly backwards. Different clouds, always, same as the sky above now.
No matter how you play with your past viewer, if you go before "last Thursday" you will see infinite time.
In the mean time, the universe came to exist Last Thursday, and while the universe, extrapolated that you can view, has infinite time.
Let's even say that I being the clever asshole that I am, made it so you can use your pad to view the future, too. You watch yourself fiddling with the pad for a few moments, get confused, then agitated. You see yourself scrabble frantically with the pad for a few seconds, then walk on, then you see yourself get apprehensive again, then a rock falls on you.
You get confused, and then agitated, then scrabble with the pad frantically to look into the far future that is just passing clouds and you splattered messily under a rock, eventually soaking into the ground, and then just a rock sitting on a barren plain with flaking blood falling off to be sucked down under the bizzare earth where your body went. Then you sigh, walk on, get apprehensive again, and then the rock happens.
Time goes on forever in both directions observably. Even as the creator, I can arbitrarily set "time" and see how my universe looks at that time, to infinity forward, to infinity back, assuming my system is properly scalable.
I wouldn't. Large calculations get fucky. Thankfully "you" never do. You get hit by a rock before you crash the simulation with an unreasonable request.
Never mind that for me, this is all of about 120 seconds of watching an egg spawn, a dude pop out of it, a dance of their neural network activation as all this happens, they look at the screen, and then get hit with the rock.
It's not unlike a time crystal.