Can I avoid the Sandbox?

Definitely. Before placing it in the Sandbox, Google gives every new site the initial SERPs boost. If during this short period you manage to "gain Google’s trust" by providing quality and unique content and acquiring a decent number of natural links from other sites, including authorities, you might just skip the probation period. Of course there’s nothing sure here, cause after all we’re talking about Google… But this site for example has never experienced Sandbox, as one of its first articles gained lots of exposure and natural links.
Of course, the best method for avoiding sandbox is to buy an older site (could be expensive though). This will also bring the "age bonus factor" into equation, proving to be useful later on, as we know how much weight does Google put on age in his ranking algorithm.

My site is in the Sandbox. How can i get out? Help!
First of all, there’s no need to panic. This "sandbox problem" sounds worse then it is. With a little bit of work and a decent amount of patience, most of the sites will get over it. So, let’s see what every site owner should do once he is sure his site is affected by a devaluation:

build quality and most importantly, unique content. Give each page an unique title and description (Meta tags of course). Also, each post should have 250 characters (that’s just my opinion) of unique content at a minimum.

Get more trusted links. I would not recommend on site wide links (also there are others claiming otherwise), but links inside the content for old and established sites, preferably authorities from your domain.

build links slowly (no more than 10 each week

don’t get only links pointing towards your home page but also deep links. This helps your site seem less "hollow". After all, if we’re talking about natural links, it’s more then normal that other sites would link to the posts they like rather than your home page, no?

don’t panic and don’t use Black or Grey methods. Anything from spamming to buying links (except buying links inside posts, that would appear to be 100% natural, which are recommended) should be out of the question.