The ceiling and floor do more to carry the load in a stud wall than the sides do. You can use large toggle bolts into the existing drywall for your top and sides and likely be OK. Use construction adhesive and either concrete anchors or power-driven fasteners to attach the bottom plate to the floor.

If that's a floating laminate or LVP floor in your pic you'll want to take it up in the place where the bottom plate goes so that it attaches directly to concrete and you aren't trapping the flooring down.

Note that if you plan to build the wall laying down on the floor and tilt it up into place, odds are it won't fit because the tilting-up creates a triangle as it rises due to the thickness of the lumber that makes the wall taller than the ceiling as it comes up. Make your wall a hair more than 1.5" shorter and use a double top plate. This also makes the toggle bolt method easier because then you can worry about fastening just the first top plate directly to the ceiling by itself, then slip the built wall in underneath it and nail to the top plate. Use shims to make it tight.

Also double check your height along the entire wall. Never assume a basement floor is flat or level.