The biggest, lowest hanging fruit thing you can do is tell them you are only interested in working at startups and you are only applying to startups. You need this in your resume, linked in profile and also make sure to mention it during the phone screens and onsites.

As an engineering hiring manager for (mostly) startups, I love candidates that have both BigCo and TinyStartup experience. Diversity of thought and usually by then, the candidates have a sense of where they want to work.

If you find that your tech or skills or experience don't line up with startups then you may have some work to do.

Most BigCos need specialists. Most Startups need generalists. Depending on your field, you might need to study up as some other posters have mentioned. I wouldn't study haphazardly however. Apply to a few startups (or industries) you are interested in and take notes of the questions they ask you and especially the questions you struggle to answer. Those are the areas to spend your time getting up to speed on.