Did Descartes really think?
For the purposes of his proof, yes:
Dubito ergo cogito ergo sum.
The witness of a doubt is the witness of a thought is the witness of a thing, hence a thing must exist.
Descartes at that point in his argument doesn’t make any assertion to the nature of reality, merely that each of us can be sure that something exists, even if our interpretation is completely wrong: the very act of doubting existence is witness to existence.
People project their own model of self into those terms, but it’s merely trying to make a broadening categorical argument and not a particular interpretation of what the objects normally represented by those terms are or how they behave (eg, times exists).
A static Descartes with the experience of currently doubting is sufficient witness for the proof, which Descartes would have himself experienced directly — the cogito is a witness to that experience of Descartes.
Classically, we understand our neurological arrangement to be a function of each last instant's without discomfort. It's another thing entirely to consider how we might have been arranged from wildly different previous states.
Although there's no compelling evidence to support it, neither is there a way to disprove it, I'm afraid.
Of course, it's not particularly useful to consider the Boltzmann brain version of yourself because a Boltzmann brain's decisions don't have any consequences. Time is better spent considering decisions by the consequences of the human taking them. Maybe this implies that you should choose to define "yourself" to refer to both your mental state combined with the ability to make decisions of consequence, and then you can safely disregard the strange kinship you may have with a Boltzmann brain. Though now this line of thought invites interesting questions about how to define what makes a decision consequential, and what exactly makes human decisions consequential...
As you are very likely familiar with the 2-slit experiment, I am of the view that 'information' [?] flows from both directions of what we perceive as 'arrow of time'. The act of choice constrains the possible pathways and that reduction is what we call 'state collapse'. So without measurement at the slits, all possible pathways are active and naturally we perceive them as an 'interference pattern'. As soon as we close the door on 'choice' flow from 'future' has no other possible path way other than the single open slit. This we note as the 'particle' modality of the experimental setup.
That answers the so-called 'paradox' of the experiment but still doesn't address why we perceive an arrow of time going forward. Now returning to the 'discreet' aspect, I posit the 'computation' of the 'virtual smooth construct of perceived reality' is what we are registering as a forward movement in an inherently timeless universe. It all seems to be inexplicably bound up with the phenomena of consciousness.