Could spacetime be flat?

Yes it would be flat. However it is impossible to remove all influence of gravity because gravity has no bounds.

 

Always curvature, and always mass. In other words, both sides of Einstein eq. The cover of MTW is wrong also. Idealized Minkowski manifold is a tangent space to pseudo Reimannian manifold. Also try to define mass in Minkowski spacetime manifold; some modes are at infiniity.

 

Even though you can imagine and even work with the Minkowski space-time, it is limited by the size of the universe which is finite. It occupies the space of about R=c*T where c is the light speed and T is the time since the big bang. there is no sense to speak of space where the matter or light has not reached yet.

Bob.