If you are looking for something to dig out the ground for the curbing, like was suggested a single "bottom plow" like farmers plow and turn over there field could work, or maybe a "potato plow" kinda like a wide sub-soiler ...
My suggestion would be to not have the concrete any more than an inch higher than the ground, less is better ...
I used my loader bucket for a little ditch ...
View attachment 5138919
Then drove my tires up it to even it out ...
View attachment 5138920
The next year, I re-did it with the backhoe ... Even had a "inspector" go down and check it out!
View attachment 5138922
