So most Physics and Scientist believe that time began in our universe when the Big Bang happened?

Very interesting question your propose.

I'd start by mentioning that TIME is simply something we've gathered to maintain a schedule. We meet people at a certain time, day, etc. So, in essence, time is already meaningless. We only consider time purposeful because of it's utility to us.

After the Big Bang, as gases condensed and planets formed, "time" began. As an ever expanding universe continues to expand, it's thermodynamic capabilities will eventually diminish (heat). "Time" would continue, but life may not.

It's all speculation as to what could happen. I would propose, what happens if eventually an entire galaxy gets sucked into a black hole, will it implode (like the big bang) and then restart time?