Stephen Hawking and Jim Hartle 1983 suggested that the Universe is finite but does not have any boundaries. ("Wave function of the universe", Physical Review vol D28, pages 2960-2975) So far, all observations and calculations agree with this. There is no boundary and there is absolutely nothing outside this nonexisting boundary. A finite number of stars in a finite universe. (I have no idea if this contributed in a constructive way the way I had hoped.)

On request, on "no boundaries": "No boundaries" is a mathematical boundary condition, which seems to be correct compared to what has been observed in fluctuations in background microwave radiation. I cannot draw any physical or philosophical conclusions of this, myself, unfortunately.

Most important though, and the commonly accepted solution to Olber's paradox is that the universe is so young that only a tiny fraction of all light has reached us yet.