You'll need to explain what you mean by 'more powerful' in this context - non-conscious processes do the vast bulk of cognitive 'heavy lifting', and conscious processes are dependent on them (see Kahneman's book, '
Thinking, Fast and Slow'). As for pre-existence, autonomic brain activity precedes the development of awareness of self in infancy, and prior to that the evidence suggests only some basic level of unreflective, present-oriented consciousness. Pre-term, the thalamo-cortical axis and neural circuitry to support consciousness aren't fully developed until the 3rd trimester, by which time a variety of other pathways are well established and active. So by any reasonable interpretation, consciousness arrives later - which is quite in keeping with its dependence on non-conscious processes.
That's true, but has no bearing on which precedes the other, and the power of consciousness is
dependent on subconscious processes, and conscious processing is qualitatively different - that's the point of it. Subconscious processes (system 1) are intuitive, fast, automatic (effortless), stereotypic, and heuristic; conscious processes (System 2) are deliberative, slow, effortful, and lazy. System 2 does as little as it can get away with (because it's slow and effortful) - mainly activity monitoring and coordination, and long-term planning when necessary.
You should be able to spot some of that by introspection - the little everyday mistakes you make because your conscious attention wasn't engaged on a task; or the words or names 'on the tip of your tongue' but inaccessible - if your conscious was in control, you'd be able to consciously retrieve them, but instead they'll pop into your consciousness later, when you're thinking of something else; that's subconscious retrieval processes at work, no longer suppressed by clunky attempts at conscious access.
You need to get past the idea that consciousness is the big 'I am'; it isn't. It gets no access at all to the vast bulk of what goes on in your brain, and what it does get is a limited summary on a 'need to know' basis. In the absence of information about the reasons behind much of our actions, it uses a narrative generator to make up plausible post-hoc explanations. A conscious self is a convenient reflective summary, a way for the whole 'you' to represent itself in the world. It may seem weird and counter-intuitive, but there's now an extensive body of empirical evidence that this view is broadly correct.