Had mass never existed, the universe would still have existed and it would have been at absolute zero. 

 

Nothing has to occupy space for that space to exist.

Had mass not existed and the universe was at absolute zero, it would still be at absolute zero and mass would still not exist.

 

Radiation and energy in general are products of reactions between particles that have mass. Neither can exist without the existence of mass.

 

Since mass has always existed, so has radiation/energy.

 

If mass and energy/radiation had never existed and the universe was still at absolute zero, time would still pass.

 

Nothing needs to happen for time to pass. Nothing needs to exist for time to pass.

 

Time as humans use the term is made up based upon what humans can observe happening. It passes whether or not those observable things happen.

 

You can not time travel. Time does not stop if you go fast enough.

 

Your rate of travel explains that if you think about it.

 

186,000 miles per second. 186,000,000 miles per second.

 

The second still passed you just went farther.