Welcome to the forum as well, BIGBRANDO
What is the model number of the compressor? Unless, you already have the pump curves that we can use to figure out the cfm at depth.
To reach a 12' depth, the compressor will need to produce at least 5.33 psi again just to reach the depth. In 3/8" line, pushing 250', the friction loss will need to be added to that 5.33 psi to achieve what the total psi will be. Then you can take that number and see what the cfm will be on the pump curve at the total psi needed.
What is the type and requirements of the diffuser you will be placing in this pond? Do you have the turnover rates at the depth of 12 feet for this unit?
By calculating the total volume of your pond and knowing what the circulation rate is of the diffuser, you should be able to calculate if you will be over aerating or worse underaerating. Unless you are trying to keep a plankton algae bloom, overaerating will not hurt the pond since really we are ciruclating with the bubbles and not injecting pure oxygen into the water.
As Theo stated, with this pond be basically Mesotrophic (NEW) the oxygen demand is low. I would not worry about the start up and introducting a large amount of "bad water" since it probably does not exist. The only way to know for sure is to use a oxygen meter.
If you have any more questions, I'm sure one of us will be here to help you.
