Although I'm a space game diehard and especially a fan of anything that eschews the "warporn" that seems to make up the vast majority of space games, I'm having trouble giving feedback. Your idea is quite amorphous. I like the newly born universe and potentially strange pockets of physics as well as the idea of player persistence. I think such a grand setting may struggle with having a grand purpose. Open-ended exploration games can be beautiful in their initial freedom then deadly boring once you exhaust the creative possibilities. With such a positive focus, what about casting the player in the role of curator / protector of this universe, maybe something like the Monolith from Arthur C. Clarke's 2001? Maybe you're some sort of evolved consciousness exploring this universe from another one, and being so far beyond your biological sensibilities you only gain by engineering space-time, uplifting life and discovering the nature of the new universe (which could be inhabited by volition at a fundamental level).
Just to further elaborate, you could take the angle expressed by some cosmologists that the universe is inimical to life. Radiation, vacuum, cosmic debris, shifts in the state of matter itself all might be said to constantly threaten life, and life through war, ignorance and stupidity threatens itself. You could make a potentially very poetic game out of being a force of good in such a setting, as the player can't be everywhere and can't save everything, which maybe adds an element of strategy. Depending on how hard you want to make the science, your choices could span millennia, and your actions would shape the universe over epochal time.
Even if that's not the direction you want to go it's an interesting idea. I just hope you veer away from some of the cosmic physics puzzle games as just minecraft with stars in a meaningless cosmos devoid of life would be disappointing.