Matter hardly moves. It doesn't "get here ahead" of anything, it was always more or less where it is. Light, including the oldest, comes towards us from all over the universe. So naturally there is some arriving now, at this moment. Look at the 2D toy model: just google "wright balloon model"--it is so easy to understand! As time goes on, the ancient light reaching us will come from matter that is farther and farther away. It will have taken longer to get here, and its wavelengths will be stretched out. But some will always be arriving. And it will always be light that was emitted at the same moment that today's oldest light was. The moment 380,000 years after the start of expansion, when the hot gas filling the universe became sufficiently transparent (due to expansion and cooling) to let the light set out on its journey. Matter being approximately stationary (e.g. galaxies moving only very slightly relative to ancient ight) does not prevent DISTANCES from expanding. That's what spacetime curvature is about. Spatial geometry is dynamic. It doesn't mean that anybody, any galaxy, is GOING anywhere. About matter moving...what started out as hot gas with only very disorganized motion has picked up a relatively small amount of more organized motion by falling together. Galaxies and stars within galaxies have comparatively small speeds (a few hundred clicks of individual motion) acquired because random patches in the original gas had slightly more or less than average density and stuff began to collect and fall towards overdense regions. It's not an issue. Although complex structures have developed over cosmological time, matter is still on average roughly stationary and evenly spread out. So you should be shot for asking "how did our matter get here ahead of the ancient light?"