How could time only have started with the Big Bang? I understand that before the Big Bang time (as well as dimensions) didn't exist. But how could this be? If there was no time then nothing could change, and so time itself couldn't come into existence.
This is both a physical and philosophical question because it depends what you mean by "time".

From a physical perspective, time doesn't really exist. We know that things change, and we measure a rate of change in relation to other things that also change (like clocks) but how we define time as an absolute concept is not something we have a firm answer to. It may not exist at all. To understand the details fo this you need to learn a whole lot of quantum mechanics, string theory and theoretical physics in general, which will take about a decade, two degrees and a doctorate. Alternatively, I've been reading a great book called "The Order of Time" by Carlo Rovelli. He is a theoretical physicist who has worked for decades to understand this stuff and then written all about it with hardly any maths and some drawings of Smurfs. I would highly recommend it.

Also, from a more philosophical perspective, if the Big Bang started with a singularity in which time and space and all matter were compressed into one single point with no dimensions, then that point contained no information about what was before it. If we can never know what was before the singularity (or even if there was anything before), then there is very little point in discussing it, so we can choose to set that as the zero point of time and call it the beginning because anything that happened before that is irrelevant. Like starting a stopwatch to time a race when the cars set off - there was time before, but that's not important for the race so we call the start of the race a time of zero.