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Consider getting in touch with a venture capital firm that specializes in technology startups. Often, it doesn't make sense for each company to have a full-time analyst. Instead, it makes a lot of sense for the VC firm to have a handful of analysts that work part-time for a number of the portfolio companies.

I've worked at a couple VC-funded startups where the VCs had us hire one of their analysts part-time. The only catch is that you must prove yourself to the VC firm first, which usually requires a strong track record and good networking skills.