God, explain this

I'm extremely religious, and the meaning of "day" is incredibly unclear. I have no problem with God's days being billion-year-long creative periods.

This makes sense, as the original text used a word that means "a period of time" and might be more accurately translated to "era" though it does not usually mean a long period of time, such as "era" usually means

Maybe "period" would've been a better word but considering the modern definition I think it would've been changed anyway

It's typically considered that day represents the normal period of time a day lasts, so about 24hrs. There are arguments for different amounts of time but with no reason to suspect that day means something completely different than when it's used in other similar parts of the bible it seems the best definition. To answer the original question there was still a lit portion of time and an unlit portion of time. Hence a day. This would be the first linear example of "time" that we all use today. So solar system not required. Of course if you have the ability to create everything from nothing and at the same time create all the laws that govern our universe I'm sure you'd also have no trouble creating a tiny little solar system that mimics the time scale you already established.