There is a difference between determinism and predestination.
But, if you are sincerely interested in exploring this seeming paradox, you might like to listen to Skinner's lecture
"On Having a Poem", in which he compares the creative process (whether composing a poem or voting on this thread) to childbirth; the mother's womb is the locus for the intersection of two genetic lines. Nothing she can do will change the genetic makeup of her child, and she does not actively choose which of her genes (or his) contribute. Is she creating a new life? Or acting as the locus where two existing strains of life merge to
continue a chain? Likewise, Skinner would argue that what we see as an act of creation is better seen as our acting as a locus for multiple lines of determination in our environment.
As far as begging the question...it would indeed be a strange sort of begging the question. Behavior can be (is, has been for decades) shown to be under the lawful control of environmental contingencies. We can (and have, countless times) systematically changed the environment and noted the resultant systematic changes in behavior. We can demonstrate that an individual need not be "consciously aware" of these changes to be affected by them, so the fact that we "feel like" we are acting autonomously is not evidence that we are doing so. Of course, you are right--we cannot trace the causal chain back infinitely. It is a chaotic system, sensitive to very small differences. Even when we can demonstrate that a small change in one environmental factor has effects on behavior, we are ignoring countless others (especially in the very rich environments humans live in). One could always point to an unmeasured factor and say "but you have not demonstrated that
this one has an effect." Sure. It could be that through some chance, or systematic error, we have only investigated things that appear deterministically related, and there are a whole slough of other things...but the thing is, the stuff we
have investigated
does influence our behavior. It is not simply begging the question. These experiments could have turned out to show
no lawful relationship of behavior to environment. But...