The universe must have laws - it could not exist without them. There is no other way for the universe to be (than to have natural laws). The laws themselves could be different to the ones we have, and if they were, we would not exist (but something else would). This does not require an intelligence to create the laws, the laws just are. 2+2=4 regardless of whether any intelligence exists to realise it. Nobody had to 'invent' the fact that 2+2=4, it just is. The laws of physics just are. Natural laws do not require a law maker - using man-made laws to claim that they do is a false analogy (a logical fallacy).
As such, to postulate that either life arose by 'chance' or was 'designed' is a false dichotomy (another logical fallacy). Natural laws influence what happens, making some outcomes more likely than others. It is not random, neither need it be intelligently controlled. For all we know, the probability that life would arise spontaneously given the laws of physics in our universe could be 100%. Or it could be 0.00001%. We don't know, because we don't know exactly what happened or how it happened. Either is fine, and neither requires an intelligent agent. Occam's razor should indeed be applied, but the existence of a supernatural intelligence greatly complicates things, since you then have to account for its existence - and the only way to do that is with special pleading (another logical fallacy).
The universe is reckoned to be about 13.82 billion years old btw.