Hello

Yes of course.

You can persue PhD right after the BSc degree. But one has to be extremely good at basics of the undergraduate syllabus. He/She must have read the standard books written by well known authors. This will definitely help facing the entrance exam conducted by the institutes.

One can check the websites of IISc Bengaluru and TIFR Mumbai for these integrated PhD programs.

As of I know these are two prestigious institutes which offers integrated PhD programs in India.

All the best.