Everything has a common origin. For me, I say that the origin is God. He has existed *always*. So my amended point is that everything other than God has a common origin, God. This is as far as I need to go. God's purpose in creating everything else is whatever it is, and His means of doing so were and are whatever they were and are.
In terms of cosmology, this is contested at least in some way on the basis that we only know so much about the origin of our own universe up to the singularity/big bang. Assuming we could make projections in some way beyond that, it does beg a question of infinite regress and a final conclusion to it being a logical necessity. The problem with your claim is that it seems to entail special pleading for an anthropomorphic entity that is remarkably similar in its general properties to humans: it ascribes purpose to things it creates, it makes ethical judgments and proclamations, etc. I would not have a problem with a nonpersonal ground of being, like Paul tillich's theology, albeit it's still unfalsifiable and to an extent unnecessary to a complete metaphysics, since absolute metaphysics would render the discipline pointless, especially if we had certain proof of its truth.
Or....
Everything has a common origin. There is no God to have created anything, so how did everything get here? This is where I have difficulty. Before I was saved, I attributed everything to randomness. It was the most sensible solution I could find that did not break down under questioning. It meant that *stuff* (stuff being the pieces that everything is made from) existed, but randomness was the force acting upon them. Now, I am sitting on the other side looking back at it, and it seems to be loaded with difficulties.
The difficulty here is presuming everything had to be created in that it comes from nothing. If we assume there may have been some chaotic matter prior to the universe and some quantum entity manipulated it, it makes remote sense. The universe itself is not strictly random in that things aren't predictable, since clearly we're not in any real danger of our personal computers exploding as we type our messages to forums or such. The quantum fluctuations or such may have a factor on a subatomic or otherwise unseen level, perhaps the cosmic level to invert things.
As a nonbeliever and naturalist I do not attribute things to randomness, especially not physical things. Interactions or friends or the like could be connected to chance, but that's not the same thing as basic physical and natural laws. You and I interacting here is admittedly random, but the processes that govern the devices we use are not random, but quite predictable.
The difference might be between innate physical processes and laws and coincidental interaction between physical beings that also have the capacity to think and judge, creating interpretations of agency and purpose behind otherwise random events.
First, randomness is as uncertain as God: one can be proven as easily as the other. Second, if randomness is responsible for everything else existing, the times that *creative forces* (I am clearly using the term to suit my needs for lack of knowing a better way) had to line up are astonishing. In fact, it is so astonishing that it becomes even more fantastic than the idea of God.
Indeterminism and a capricious deity are certainly similar, which seems like you're equating a world with your God to a world where gasoline may or may not ignite when it encounters a spark, which would make me paranoid, if not outright insane. Your point is well met in a world of indeterminacy, but if your God is remotely powerful, then we have a world where people have not a care in the world, especially if we had some proof of this deity existing and managing the world. Either one creates problems, either because of excess or deficient uncertainty, which makes life interesting, if not a bit unnerving at times.
Before anyone gets his feathers ruffled, rest assured that I am aware that there are other options, but I do not see an option existing that does not rest on either randomness or purpose.
What, other than randomness or purpose could account for existence? Some things that I have thrown around are that everything has always existed, that nothing actually exists now, that there is no common origin and multiple sources exists, and a few other equally dissatisfying ideas
Randomness in the absolute sense would be one end of the spectrum and absolute purpose would be on the other. Both are probably fairly rare in terms of defended philosophical positions. Most people fall somewhere in between, though potentially leaning towards these two. But a lot of this amounts to the tendency of humans to find agency and purpose behind things that may, in fact, have no such thing.
A tree falling and not killing you, but smashing your house, may be seen as divine protection and have some telos behind it, but it's really just coincidence. The universe's existence is similar, though on a grander scale. It doesn't really have any ultimate purpose, nor do we. I've discussed this in a topic I may revive, but purpose as basically understood is a conceptual thing we appropriate to things, including ourselves. And this is preferable to having preset functions, which would make us automatons. A universe which is predictable, but still has no ultimate purpose is far better than either a predictable universe with ultimate purpose or an unpredictable one with no ultimate purpose.