From Public Equities to Private Equities

tldr: Does a background in Business Operations help me break into Growth Equity? 

Hi monkeys, I could use some advice about breaking into private equity. I have five years of work experience, two in equity research, two on the buy-side and about one year trying to build my own startup. On the buy-side I helped on some minority investments in private companies such as Anduril, Discord and OpenAI. However, I don't have experience with buyouts nor much on the operational side. 

I've taken some months to figure out what I want to do long-term and have come to the realization that the hands-off approach in public equities is not that appealing to me. Private equity, growth equity in specific, seems super exciting to me but I've had a difficult time breaking in. I'm not getting a lot of traction on applications, and even networking has been difficult. 

I'm in the process of interviewing for a couple of companies at the moment that I am hoping to use as stepping stones to bridge my skillset into private equity. One seems like a pretty good fit and would be as a strategic finance manager, and the other is a role as a business operations manager at a software startup. The problem is for the business operations manager role I have to accept/decline by the end of the week and I am still pretty early in the process with my other roles. My question is, is business operations, combined with my investing background, a worthwhile career step that moves me closer to growth equity?