Time and space are qualities of nature defined by the gravitational field, not by some background 'thing' in which gravitational fields are embedded. Space and time are the physical components of gravity.
When we study electromagnetic fields, we represent these fields by changes in their electric and magnetic components. When we study the gravitational field, we represent it by changes in space and time.
If suddenly the gravitational field of the universe was shut off, space and time would cease to exist.