Help changing direct hard-wire to outlet for new dishwasher
I think your methodology is sound. You want to make sure the plug and outlet is accessible so putting it under the sink is the way to go. When you mount it be sure to secure it to a stud and away from anywhere that could be exposed to water. This means away from the shutoff valves and not directly under the sink supply connections. Cable straps will hold the metallic cable in place. Make sure that you use enough straps that the cable is secure to the wall studs under the sink and not loose or attached to the flooring. Based on your picture you can probably do this without trimming the cable.
Take out the appropriate knockout and using the connector to secure the cable run the cable and wires into the box. Secure the connector with the locknut. Connect the hot (black) wire to the brass screw and the white to the silver. Green goes to the ground.
You shouldn't need a GFCI on this but check codes.

Edit
Many dishwashers that come with a wall plug also have alternate instructions for hardwiring. The Beko installation manual doesn't offer that as an option but you might want to contact the manufacturer to see if it is recommended.