I think iam qualified to answer this question because i have worked only in startups during the past 10 years. It actually happened by accident . But then i got so used to startups that i didnt look beyond them.
Remember, startups typically dont use traditional channels like HR to hire (happens in few cases). They typically go by their network . However there is another way. Just search for top management’s email (CEO/CTO) and write to them about your interest in the firm and how you complement their vision. It works in most cases.
I can tell you that in all the startups where i secured a job, none of the firms were actively looking for a person. They hired me because they felt i could add value.
Keep looking for new startups in your area through top venture blogs (Yourstory or Vccirle etc) and read about their markets, vision etc and get educated.
If you have an idea in mind try to implement it as a mini-project so that you can show your thought process and clarity of vision during an interview. It could be a website based project or interesting blogs in the area of the firm that you are targeting.
Last but not the least , while it looks nice to be a part of a startup firm, be mentally prepared to slog 10–15 hours a day and hit the ball rolling the day you join. Many candidates do well in the interview and join, but arent mentally prepared to handle the pressure and leave within a week. You need to be a hands-on professional and should be able to get the job done however seemingly tough it is.