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I don't think that is a realistic expectation since stars do not shine forever, and additionally we would only expect a finite number of stars to be in close enough proximity to us that their photons would have had sufficient time to reach our planet. IOW, some stars would be so infintely distant from us spatially that no amount of time would permit their photons to reach us.
But the premise is that in an infinitely large universe, there would have always been an infinite amount of time before the present.
Hence, the amount of stars that are within range of us would be infinite, and as such all of the night sky would be filled with stars.
This assumes that the stars are distributed more or less randomly, so that if you look in any direction, there would be, at a finite distance, a glowing star which light reaches us as we look at the sky.
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