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I am afraid no one knows how to avoid or get out from the sandbox earlier. The good thing is that the sandbox affects only competitive keywords, thus if your site covers not hot areas you may not suffer from it.
May be it's not a sandbox, may be it's kind of indexing queue for hot keywords. I don't know.
My most recent domain before this one, went right in the sandbox, but I was using adwords from the 3rd day of that site's launch. I've been told adwords doesn't cause the sandbox but...
Yes, there are algorithm factors that can delay new domain pages from showing in search results -- a "sandbox-like effect" if you will. But it's not like you just do your time and then get released. I've seen out in 3 weeks and out in 8 months, and both happened this January.
Here's a good discussion from earlier this month about what to do while "sandboxed" -- hope it helps: