Your background seems primed to get shortlisted
Business Analyst - I assume you're from McKinsey or Kearney
How to apply - get in touch with Michael Page recruiters or just write good cold emails to VP+ folks at target funds (ideally send it to people who invest in spaces where you feel you want to invest)
They're hiring round the year since folks leave every now and then, so you can start reaching out.
Don't worry about getting shortlisted, once again, focus on prep: read tonnes about investing, startups in India, seed/series A investments from recent years
It'll pay you better than consulting yep. Assuming you make 20-30L, you'll jump to 50-60L at a Tier 1 fund if you make it