It depends on how you define "early age" for the universe. Of course it can go on a long time, so in that sense the universe is extremely early age. On the other hand most of the stars that will ever exist have already been born, and every moment that goes by more parts of the universe move forever out of our reach due to the expansion of space. The universe may last forever but most of the action has already happened.
Early in the sense that we even got the chance to observe galaxies outside of our local group, or the CMB.
The age of star formation is mostly over yes, but not completely yet - and I believe it's figured that no red dwarf can have reached even a tiny fraction of its lifespan so far?
