Best way to get rid of vines

Had an area of our property that was overgrown. Tore it all up and and added some sand. Have to get a get a fence built before I can lay sod.

Over the last couple of weeks we have had a huge amount of weed growth poke through. About 99% of that is vines about 4-6” under the soil.

Aside from digging them up and spraying them, what can really be done to mitigate? The sobs just keep coming back. I’ve sprayed them with Crossbow and it killed what was visible but more came right back.