Smiling Buddha (MEA designation: Pokhran-I) was the assigned code name of India's first successful nuclear bomb test on 18 May 1974. The bomb was detonated on the army base, Pokhran Test Range (PTR), in Rajasthan by the Indian Army under the supervision of several key Indian generals.

When did india conduct her first nuclear test? Let's have some stream of consciousness first.
To answer this question, we should know that: Smiling Buddha (MEA designation: Pokhran-I) was the assigned code name of India's first successful nuclear bomb test on 18 May 1974. So, the answer is 18 May 1974.