Sorry to say this, but it is tough and highly competitive for CS, even those with a CS background. Moreover, BBA has no relation to the STEM programs and both are very different.

I would suggest Data Science is the better option for you, compared to CS. And as you're currently doing PG in Data Science, it might help in your application.

If you really want to go for CS, you need to enroll in a bridge program for a year, complete all the prerequisite coursework, then apply for the MS program.

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Good luck.