Rendering a whole universe of randomly generated stars amounts to a skybox. Whatever the player does in the game, it will be at a negligibly small scale compared to the displacement that's needed to notice any parallax error in the skybox. Only a few objects are close enough to require less cheap rendering.
I would prerender various skybox layers as much as possible: assuming we are around Earth, Moon, Sun and of course Earth and close space stations might need true realtime rendering; but Solar system planets could be a skybox layer (valid for a few minutes because they are moving); then individual visible stars and other small objects, valid for a large central region of the Solar system; Milky Way background, valid for a vast region of the Milky Way that probably exceeds the scope of a reasonable game; and finally close enough other galaxies. When the player goes to Mars, redraw satellites and planets and constellations as a luxury.
Quantitatively, bright objects are likely to be more expensive to generate according to fancy distributions than to render without storing them permanently; and if you have enough memory to display one skybox set and render future skyboxes to offscreen buffers you can easily brute-force billions of randomly generated stars over the course of a few minutes instead of doing something complex and approximate to draw a boring starfield in real time.