Is it possible that deep vein thrombosis in the leg be caused by a gash on the leg?

Possibly...: While the gash on the leg wouldn't 'cause' the blood clot, if the person were immobile for a period of time related to the gash then the immobility could cause the blood clot.

Maybe: Obviously if the cut was deep enough to get near the deep venous system you could get a dvt. But if a DVT were to occur it could be from limited mobility after the injury, the use of splints or there devices that can create venous outflow obstructions or anything that can slow down blood flow in the veins and cause them to clot.