This is still gene expression, AR activation you are talking about is still a genomic effect. Non-genomic effects, ie rapid effects of AAS are independent of the Androgen Receptor. That "growth" that most see in the initial first month is largely a big increase in nitrogen.
This is super heavy microbio/biochem stuff, it's very dry and even bores me sometimes, but basically, most of our growth happens during REST and RECOVERY. Muscles aren't really built in the gym, they are built in the kitchen, chair and bed when you are resting and recovery.
The gym training/weight lifting works through damaging muscle which makes your body BUILD MUSCLE during RECOVERY/repair. How does taking an AAS help you build more protein while you are damaging it in the gym? Directly it cannot.
Now if the oral AAS makes you stronger and you can get more PRs and perform better progressive overloading, that is a much more plausible mechanism for timing oral/injectable AAS for training. That is up for the debate.
Like i said, i'm not arguing for or against, i'm stating the facts, physiology and data we have regarding a theory like this. I believe personal experience is just as if not more important than studies and science. I take it all; practical experiences (my own and others), anecdotes, etc. I bet if a do a super deep dive and i might even find something on a subject like this but it doesn't really interest me that much.
"Previous work in the endocrine and neuroendocrine fields has viewed androgen receptors (AR) as a transcription factor activated by testosterone or one of its many metabolites. The bound androgen receptor acts as transcription factor and binds to specific DNA response elements in target gene promoters, causing activation or repression of transcription and subsequently protein synthesis. Over the past two decades evidence has begun to accumulate to implicate androgens, dependent or independent of the AR, in rapid actions at the cellular and organism level. Androgen’s rapid time course of action; effects in the absence or inhibition of the cellular machinery necessary for transcription/translation; and/or the effects of androgens not able to translocate to the nucleus suggest a method of androgen action not initially dependent on genomic mechcanisms (i.e. non-genomic in nature). In the present paper the non-genomic effects of androgens are reviewed, along with a discussion of the possible role non-genomic androgen actions have on animal physiology and behavior."
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2386261/