1991 Nissan 240SX not starting

If the car runs fine once started then all your fuel system components should be in working order.

Couple of ideas-
Large intake leak. You may be getting too much un-metered air into the engine causing an extremely lean condition and a hard start.

The engine also relies on the coolant temp sensor to accurately measure temperature so that it can provide the correct mixture on startup. If that sensor is open or shorted it will drastically change the mixture making it difficult to start.

Have you accessed the fault memory of the ECU? Any codes stored may point us in the right direction.

This is all assuming that your tune-up parts are in perfect working order. Make sure the plugs are the correct application, in good shape, and gapped properly. Cap, rotor, fuel filter, and air filter should also be in acceptable condition.