DMOZ is important but takes a long time. The best way to get into Google is to get linked from an existing indexed page. Automated submissions are against Googles TOS (terms of service) and will not...
Do you have a site map page that is linked from your home page and indexed by Google or do you have a page that you know is indexed and you can link to these...
Get a link from a page that is indexed by Google and you will be indexed, it will take a while for you to move up in the SERPs though, especially if your keywords are competitive.
I think the Google sandbox is a myth. New sites can take a while to get anywhere in the SERPS (search engine results pages), but I can usually get them spidered / indexed within a few weeks.