There definitely are opportunities for professionals with non-engineering background in the software testing / IT.
Software testing job will require you some prior knowledge of how testing works in the software industry. I recommend exploring the multiple segments that exist in the industry, build your specialisation in one or two before applying to job.
If you dedicate your time to it, you should be gain sufficient expertise within 3-4 months. Here are a few domains that I suggest:
- Database testing
- Stress testing
- Web App testing
- UI testing
- Hardware testing
- Device-driver testing
Without prior experience, I suggest that you should aim for building some experience in manual testing. Manual testing will give you a clear idea of the real-world testing.
The second step would be to build some expertise in automation testing. Selenium with Python or Selenium with Java are heavily in demand in India. If you can join any reputed institute - you should be able to gain some experience fast.
I also recommend opting for basic certification like ISTQB. It will give you an edge in the job market.
I hope this helps. If you have follow-up questions, ask below.