I concur with redrock and nemo123.
I didn't apply to NIH SIP, but I applied to two Amgens and a SURF this past summer (ultimately accepted to one, waitlisted at another) and what was instrumental in my case was e-mailing PIs around December/January. Typically, "announcements of opportunity" are submitted by the PIs at the start of the new year, but some labs I knew of were hunting for potential applicants before then. Caltech even required you to submit a proposal with your potential mentor as a part of the application, so in that case it was essential to forge a connection.
Prior to applying I only had 1 year of research, spread across two different labs (nothing really remarkable) and my home institution is not a research powerhouse. Every Amgen scholar in my cohort had previous research experience, but many of the participants in the other summer programs (SIP, SURP, etc.) did not have any.
I guess the best game plan is just to cast your net wide? Maybe check with professors/mentors at your university and see if they have any connections (or previous students!) that they know are hosting summer research students. If you have any unique research skills, play that up because many PIs would love to take on someone who would require minimal preliminary instruction; ten weeks is far less time than it seems... especially for bench research.