It would be way easier to add edging to a board, rather than to rout out a pocket in a single, monolithic piece of wood.
To connect edging to a board you would first cut 45-degree angles on each of the 4 pieces of edging (if you have a mitre saw). To attach the edging to the main board there are multiple options: (1) glue, (2) biscuits, (3) dowel pins, (4) nails, or (5) dovetail (fancy). You can also make a rabbet in the main board and a matching rabbet on the edge pieces with a table saw. This will make for a firmer joint, if desired. One advantage of making a rabbetted joint is that you can screw the edging in from bottom, so the screws will be hidden. The basic idea of rabbetted joint is shown below:
Note that you can either cut the rabbet from a single board, or just screw boards together and get the same effect, which is even easier.
To mill a pocket, normally a woodworker will use a router and then chisel out the corners. This is necessary because a router has a round bit, so the corners will be rounded. To make them square, they need to be cut out by hand with a chisel.