2. Hop on AngelList (angel.co) and scour through startups in your area. Identify 10 that you're interested in and why.
3. Reach out to the team via LinkedIn or AngelList with your request + what you're hoping to learn from the internship and why them. Invite a team member for coffee or an intro call
4. Goodluck :)
I am biased, but speaking from my experience at RedHat in Czech republic, from time-to-time I would see interns doing university outreach, in our finance department and some taking care of our facilities. Technical-writing might fit your bill as well.
I would look for open-house-days, or local conferences where employees of your chosen corp would present. This might give you a better leg into their doors than just spamming their generic CV inbox .
Why would you seek non-tech intern position at a startup then? As another commenter mentioned, you're likely better off looking for an internship at a larger company, as there may be more going on to observe and learn from.
Most interns end up doing a lot of time consuming stuff that requires some basic understanding of the business but not much skill or experience - like researching sales or PR leads and filling out spreadsheets with that info.
Some startups have interns run their social media campaigns or fill in when customer service load is heavy. I’ve also seen an intern tasked with writing first drafts of blog posts and white papers that a founder had been meaning to get to for months but couldn’t find the time.