Contextually the mist that went up was a phenomenon which happened during the week of creation, specifically on the third day. However, in conservative Christian doctrine this condition persisted until the time of Noah.
We have to deduce a physical process by which a solid ball of stratified sediment, the Earth at the end of the second day, is formed into a hollow sphere with a hydrological system by the end of the third day.
The fountains of the great deep are channels through the crust and mantle of the original Earth through which water drained into the great deep. They were later used to flood the Earth in the time of Noah.
If we're going to live with the Lord God who's going to reign forever and ever, and a pure river of the water of life is flowing, then it must be cycling because God isn't going to constantly create new water forever.
We're going to ignore the possibility that Psalms 42:7 is flowery poetic language intended to teach us something spiritual. Instead we're going to use it as the description of a hydrological system in a test of Hypothesis 22.
The deep and the great deep are both translated from the same Hebrew word, tehom. The difference signifies a transition from the deep where Earth was created to when the great deep is in the interior of the Earth.
We have to know the end from the beginning and the beginning from the end. When we understand beginning and end we can see that they are conceptually, and to a great extent physically, equivalent.
The Millennial Kingdom hydrological cycle is a reestablishment of the original condition of the earth, when Eden was at plateau at the top of a mountain that filled the whole Earth.
Ezekiel tells us that a great river will issue forth from the temple in the Jerusalem. This is part of a hydrological cycle which doesn't presently exist. It's established along with the Millennial Kingdom.
Can we by searching find out God? The clear implication is that no, we can't, but there's something important to remember whenever we contemplate passages from the book of Job: Who's speaking?