Yeah I'm positive that non turbo supras do not have an oil cooler. That is what the oil cooler is for. The extra heat from the turbo.

Check the TSRM page LU-13 if you don't believe me. Oil cooler and Relief Valve 7M-GTE ONLY.

Your oil filter housing is totally different than a GTE. You have no feed from the filter and no return on the passenger side of the oil pan. Get a GTE oil filter housing, oil pan, oil cooler and lines and you can run an oil cooler on a GE block.