1. The Universe was smaller way back then.
2. Light was faster way back then................
On your second point, 2. Light was faster way back then................, would imply a medium exists which affects the speed of light which violates Einstein's long established relativity theory - no?
On your first point, 1. The Universe was smaller way back then. What if the universe was actually larger back then? What if instead of expanding, the universe is actually contracting, growing smaller at an ever increasing rate like expanding foam, but in reverse?