I agree to part of what you said. When we see starlight from a galaxy 10 billion ly away, we must conclude that it has existed long enough for that light to have gotten here. We must conclude that the universe is old. When we ask how it got there and only use observation to find the answer it starts getting a little tricky.
We've never seen matter created. We suspect red shift means expansion so we conclude a big bang. Our observation still never tells us anything about where the galaxy came from or why.