Here's a (probably stupid) thought: doesn't the existence of the present proves that matter has not always existed?
For matter to have always existed, historical time must be infinite. This means that the current present moment is an infinite amount of time in the future from a point sometime in the infinite past.
Infinity cannot be reached however, by definition. Therefore it would be impossible for time to progress to the present moment, since we are located at a point in infinity on the path of time. In the same way, we will never reach an infinite future.
Since we are here, in the present, which has obviously been reached, the past is therefore finite. Which means matter cannot have an infinite history.
Alternatively, time is infinite, and anyone you meet is a product of your own deranged imagination.
Next week: the Douglas Adams proof that the population of the universe is zero.
Expatbrit