If consciousness is just awareness, then we already exist in a world where consciousness is non-biological. The standard device is the thermostat. Any electrically operated device is aware of the power coming on and conscious that it needs to now perform its function. A rock is conscious or aware of rising temperature and thus expands; of a hammer blow and thus shatters; of acid poured on it thus causing a chemical change, etc.
Probably what is really meant here is consciousness that is aware that it has consciousness, or self-awareness. Such an entity, among others, is the human being. Human beings have self-awareness.
Probably what is meant here by a non-biological process is evolution of self-awareness that does not arise by natural selection, via Mother Nature, but rather by artificial selection, which might beg the question if whatever provides the artificial selection was the product of natural selection in the first place. If Mother Nature naturally creates the human and the human in turns creates Robo-Raptor, is it incorrect to suggest that Mother Nature ultimately created Robo-Raptor?
The natural selection of self-awareness is formed around CHON - Carbon, Hydrogen, Oxygen and Nitrogen - and the various complex chemicals, organic chemicals, and bio-chemicals they can produce to form structures that ultimately have self-awareness. Presumably such self-aware entities could artificially select new-and-improved self-aware entities by mixing CHON in a test-tube. That could result in a self-aware consciousness that wasn't the product of natural selection. On the other hand, that's probably not what is meant either by non-biological self-aware consciousness.
The implication here is the artificial selection of a self-aware consciousness via substances and structures that aren't CHON.
The question arises, is there really anything super, ultra, magical about CHON? I mean it's all just quarks and electrons and the various forces that produce what we call chemistry. If Mother Nature can evolve self-aware consciousness out of CHON's quarks and electrons and associated forces, what's the big deal in humans artificially evolving a self-aware consciousness out of the rest of the 88 naturally occurring elements available for use out of the Periodic Table, elements also comprised of quarks and electrons and responsive to the various fundamental forces?
Mother Nature operated without a goal, without direction, without any instruction manual, without any foresight, without any intellect, doing chemistry experiments totally at random, using all those readily available common materials within reach, and ended up producing, among other things, self-aware consciousness.
Surely a self-aware consciousness, operating with a goal, with direction, with a basic instruction manual, with foresight, with intellect, doing chemistry experiments in a deliberate structured manner, using all materials available, can produce a non-CHON, non-biological, self-aware consciousness. No one says it's a walkover, a piece of cake, something any kid could do with a home chemistry set, but it's surely not impossible, eventually.