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).
The player being an evolved consciousness from another universe is in line with what I have in mind for the game and fits well. Bringing up life and inciting activity as a means of discovering/enabling more of the universe sounds exciting to me, and indeed could be part of the solution to the inevitable boredom of exploration games, without casting the player in an explicit role.
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.
This would be a good counterpart to players bringing up life, and a way to bring synergy between player persistence and the logic of the world. Whereas I previously thought player persistence to be almost "fluff", this approach makes it more meaningful. The tension between life and death would be very obvious as all player's efforts are combined to reveal more about the world, which is perfectly in sync with my core ideals for the game.
Thank you for your inspirational input, Wavinator. Every reply helps me solidify parts of the design.