It depends on why your submitting the design. If it is unsolicited it is a different avenue then if it is through a Broad Agency Announcement (BAA) which of course is different than a SBIR. Of course, it also depends on what your attempting to gain from your submission, if it isn't solicited then you might not get anywhere with it no matter what avenue you approach. If it was solicited, then you’re late and you probably won't gain any attention from the sponsors unless they plan on releasing the SBIR again during the next submission quarter. Most agencies are also very particular that you follow the particular submission approach require.
My advice is that you find a contact in whatever branch of the government your idea is for and see if you can speak to someone directly. If you have a unique idea, it is possible that the individual will sponsor a SBIR based on your concept.