how thick is the concrete?
The fixing really only needs to resist shear (sideways movement) as the wall is unlikely to recieve any upwards stresses. Bearing this in mind you could drill through the sole into the concrete but only far enough to set some studs with epoxy resin. When the resin is dry you can spin a nut on and tighten it up. Even just 30mm will be plenty provided the stud is a tight fit in the hole and you clean out the dust before using the resin.
I can see this as a potential solution.
If there's a screed, the easiest method is to use masonary nails. No screed, just concrete, then screw and plug. Personally I would use dpc under the plate.Steve
Not sure how much of a screed there is to be honest, or even whether it is simply rubble under a screed of sorts. My money is on a cheap job, whatever it is.
Why not screw 10" x 6" zinc batt plates to the underside of your sole plate. Then fix screw thro the overhanging plate to the floor. You still use a dpc too..
something like this
Yeah, another option.