As an organization administrator, I can say that students who turn up now and get past the initial hurdles, prove their mettle, etc. are much more appealing than students who submit a proposal at the end of the application period.
When you interact with an organization for a while, you also will get a better feel for what kind of projects are available and what interests you. You may even think of something we haven't and that should make the project even more appealing to you.
Get involved early and stay involved afterwards.
--joel
RTEMS