Hawking explains cosmology for general readers: the Big Bang, black holes, space-time, and the search for a unified theory explaining the universe's origin and fate.
Time is not separate from space. The two are woven together into one thing, space-time. If time is a property of the universe itself, then asking what happened before the universe began has no meaning, because there was no 'before'.
We don't see disorder increase because time happens to run forward. We call 'forward' whichever direction disorder grows in. Memory, like a computer's, can only record things in the order disorder increases, which makes the rule that disorder grows almost true by definition.
A scientific theory is always a working guess. No number of experiments that agree with it can prove it, because the next result might contradict it. Today's obvious truth could one day look as silly as a world resting on turtles.
Before the twentieth century, no one suggested the universe might be growing or shrinking. People wanted eternal truths, and it was a comfort to think the universe lasts forever even though they grow old and die. Many still dislike the idea that time had a beginning, because it seems to invite a creator.
Science has steadily found that events follow an underlying order rather than happening at random. Saying the universe suits us simply by chance, or because we are here to see it, gives up on finding that order. Even a complete set of laws would still leave open why there is a universe for them to describe.