One way would be to cut up a piece of 12- 18 mm ply or MDF into a strip about 75- 100 mm wide on the table saw.
Then cut this strip into four lengths. Two pieces will be the length of the short sides of your planned rectangular cutout.
The other two would be the length of the long sides of the rectangular cutout plus twice the width of the strips.
Join the ends of the short strips to the long edges of the long strips precisely at the corners. You can join the corners with biscuits, dowels, a loose tongue worked with a router, even just glue the butts together at a bit of a push-- that might be a bit risky though.
You will have created an inside rectangle that exactly matches your planned cutout, a jig.
Attach the jig to your piece of 6mm MDF. Bore a generous hole through your MDF that almost touches your jig. Fit a top bearing pattern cutting bit in your router. Lower it through the pre-bored hole and, ensuring the bit doesn't accidentally touch the edge of the bored hole, switch on the router. Move the router towards the jig until the bearing rubs on it. Then work clockwise around the jig until the cutout drops away. Don't go anti-clockwise because that would be a climb cut that could cause the router to run away from you.
If your router isn't powerful enough to do this in one cut you'd be able to do essentially the same job by making a similar jig, but in this case you'd set it up with an offset to use a guide bush attached to the router base along with a straight bit.
This way you could achieve the cut in two or three downward steps. For example, if you use a 25mm guide bush with a 12 mm cutter the offset of your jig would be 6.5 mm greater all around than your required cutout, i.e., if your rectangular cut out must be 600 X 300 mm, the inner rectangle of your jig will measure 613 X 313 mm. Slainte.
