Can't shift when cold. Need some assistance from a supra expert! :(

[MA70-3.0GT]

From what I recall with driving mine, (getting on couple of years ago now ) with the autobox, from cold the gears shifted differently & when I looked it up I seem to remember that the gearbox ECU had an input from the coolant temp. sensor so that it kept the revs down until the motor started to warm through...

Could be a JDM only thing since mine's an import, but makes sense really, you don't thrash your manual cars till the motor's warm so the electronics do the same for the auto?

As far as the OP's question goes, I guess it's a manual box as you talk about the clutch?
That being the case, can you put it in first with the engine off & then start the engine with the clutch pressed? It's possible the clutch or hydraulic system has a problem but I'd think it's worth checking the gearbox has the correct grade oil in too as a heavier oil wouldn't help when cold...
Also, this is the reason why you should generally make sure you get to view a potential purchase from cold, if it's been warmed up there's ALWAYS a good reason they've done it apart from "popping to the shop just before you arrived"...