Do you believe in any sort of higher power?
None whatsoever
Are you more of a believer that the universe was an accident?
Not an "accident" as such, more a convoluted series of circumstance, and happy (for us) coincidences.
the universe exists within time, matter and space, and time matter and space all have a beginning
This doesn't necessarily follow. It's normal and understandable for humans to be prone to conceiving of time in finite chunks with a distinct beginning and end, because our lifespans are relatively short, and we organise our lives around fixed moments in time, specific hours of the day and so on. The problem with applying this to the origin of the universe is it presupposes there is only one universe, only ever has been one universe, and therefore something must have "created" it, if not just given it a "helping hand" to "begin".
It's entirely plausible that this isn't the only universe, or the first universe, or that this universe was not created out of "nothing", in fact, the assertion the universe was created out of "nothing" is highly implausible, which is why I believe our current universe is only the latest in an infinitesimal number of universes, and it's origins lie in the destruction of the previous one. If you accept infinity, then there is no requirement for a "beginning" and no need for a creator, helping hand, or anything to have existed "outside" the universe.
That last part is, in itself, an absurdity. The universe IS everything. Anything that exists does so within the universe. Things which do not exist can not will themselves into existence, and if there was something, an entity of some sort, which predates the universe, where was it hanging about? Since there is nothing, (because there is no universe yet, remember) there is nowhere for this entity to hang about. If it created the universe and the universe has a distinct "beginning", what was this entity doing before creating the universe, and why didn't it just create the universe a bit more promptly? These contradictions and absurdities can be resolved with one simple proposition - no such entity exists or ever has, because that's not how the universe "began".