Hello everyone

I have a Mazda AZ-3 (MX-3), year 1995, 1.5 ltrs, 16v, DOHC, which I recently bought as a project sport - coupe car to restore it and bring it back in the streets.
The major issue of this car is the automatic transmission. When I shift a gear with the gear lever, the vehicle doesn't respond at all, like I didn't shift any gear on it. Does the transmission needs rebuild or replacement?? Is there something that I can do, before proceeding to rebuild or replacement, such as transmission oil and filter replacement??? I mean, if I replace the automatic transmission oil and transmission filter, will this improve its performance and fix this problem, or it will not make any difference??? Any ideas or help is welcome. Thank you.