Your radio is from a 9/74-11/75 Toyota Publica/1000. It is not a Land Cruiser radio. Based on the parts catalog diagram, it did not originally come with a face plate, but was mounted through knob/dial cut-outs in the dash.
It may fit the FJ40 radio cut-out and the FJ40 OEM faceplate may fit the radio. Here's the dimensions of a later 40 radio. There
can be a couple of issues trying to fit a FJ40 faceplate on non-40 Toyota radio, shaft spacing and tuning dial off-center. If there
is a problem with the faceplate fit, it is usually because the shaft spacing on the radio doesn't match the holes in the faceplate.
Even if the shaft spacing is not a problem, the radio dial may not be centered in the faceplate dial opening.
The faceplate itself lines up with the sides of the radio and the bottom edge. It extends slightly above the top edge of the radio. I don't have this unit any more, so can not provide the exact dimensions. Note the mounting screw on the side. This fits the side tab of the FJ40 cut-out opening. Based on the parts catalog picture, your radio mounted using brackets in the back. This is FJ40 radio 86120-60020.
Details of the faceplate.