The Universe Is 13.73 Billion Years Old
Just FYI, Genesis and Psalms are two completely different types of books. Genesis is a book of history. The Creation story is a historical account of how God created the Earth. It isn't meant to be poetic. The word that is translated as "day" is only ever used to mean a 24 hour period. That is "the evening and morning were the first day." This is talking about a day on earth
Your quote from Psalms (a book of songs and poetry) is talking about a day in Heaven (in the presence of God.) A day with the Lord is as a thousand years. It could simply be referring to the fact that time will either be perceived very differently or will not exist at all in Heaven. God is eternal and is not bound or limited by time. Rather, time is limited by God since He is the Creator of it. And time is something that God created for us to live in. The point is you can't take a day on Earth and a day in Heaven and then use them interchangeably.
Does that make it more clear?
The Big Bang idea does not qualify to be a theory because, being unobservable, it fails step 1 of the Scientific Method (Make an observation.) The Creation Story, again, is history and therefore not subject to the Scientific Method. The two ideas mix together about as well as oil and water.