Why do you suppose we're here? (AKA determinism versus randomness)?

If you truly subscribed to buddhism you would not feel that your question was worth answering. You believe in reincarnation which is a hindu philosophy. Questions such as yours only open "non-Buddhists" minds into thinking they have the opportunity of understanding what it is to be alive. A true buddhist would not be concerned about our miraculous presence in front of our own eyes. As well as a buddhist would not find necessity in thinking the universe has a "why"; a direction or a motive even. Only to be appreciative of your time and to understand your value can you only give yourself a good definition of why. But, that definition belongs to nobody else but you. As a more formal answer to your question if randomness ruled, would you not expect things to disappear as quickly as they appeared randomly? Things are as they are, not as they seem. And of course you can never see things as they are, only as they seem.