The square hole is where the factory captured nut used to be.  They were swaged into the frame, but sometimes can pop or fall out.

A toggle bolt would not be a good solution.  Toggle bolts are designed to resist pullout; they don do handle shear loading well, as they will likely move around instead of holding fast.  That bolt is loaded in shear every time you close the hood. 

Anytime I've ended up with a captured nut that has rusted out, broken loose, or gone missing I have taken a page from what modern OEMs are doing.  They will have a nut secured with a metal tab that locks into the frame in a round or oval recess.  I will weld a flat washer to the nut, then weld a length of 1/8" diameter rod to the side.  I fish the nut through another hole in the frame, then either use an existing hole or drill one in the frame to locate the tab, onto which I bend a 90 degree hook to locate in the hole.

There aren't any other holes in the radiator support is the problem.  Another possible solution would be to weld a flat washer to the nut, then englarge the existing hole to the size of the washer.  Use a bolt as a handle to hold the washer/ nut in position and then fully tack weld the washer to the surrounding metal.  Grind the welds flush and paint to prevent rust. 

Weld a new nut in if you ever take it apart again.