While some aspects of your assertions are partially true, I have to say that you have missed the mark just a bit.
First, let me say that there is no sandbox, it’s just a myth. This has been confirmed by Google engineer Matt Cutts. However, there are factors within Google’s standard search algorithm that may “feel” like a sandbox and thus the term “Sandbox Effect” was adopted to describe this effect.
While you are partially correct that age is a factor, it’s not the age of your “website” that is important, it is the age of your individual web page URL within Google’s index. Old websites have their pages ranked with the exact same algorithm as a brand new website’s pages. So a new page on an old website is treated the same as a new page on a new website. The reason it may seem that they are treated differently is due to the internal linking that is typically done on a new page when it is added to an old website. If you started a brand new website and linked it to it from an established website just as you would do with internal links you would see the same result.
Google doesn’t hate new websites, I would say they love new websites and put forth a great deal of effort to find and index them. Google also values trust and trust is something that must be earned over time and only pages that have stood the test of time will have earned the highest level of trust.
Older pages will generally have earned more trust and therefore higher rankings, but this doesn’t mean Google hates new content or new websites. In fact, Google has a special feature built into its standard algorithm that boosts the ranking of new content. This feature is known as QDF (Query Deserves Freshness) and is partially responsible for the feeling that new webmasters perceive as the “Sandbox Effect”.
It seems that new or inexperienced webmasters often convince themselves that they have actually earned the higher rankings that they receive from the temporary boost of QDF. After this temporary boost wears off and their new page sinks to it’s truly earned rankings they often imagine that they have been penalized by the mythical “Google Sandbox”. It’s just their imagination running wild due in part to not knowing about this QDF freshness factor.
I believe where you really miss the mark is in your assertion that search engines rank websites, they don’t. Sites that list websites are known as “Website Directories” and are different in nature to a search engine. The primary difference in a search engine and a website directory is what is indexed. A website directory indexes websites and a search engine index individual web documents. When you don’t understand this fundamental difference it leads to incorrect conclusions about SEO test data and some really wacky SEO theories.
Search engines don’t assign PR, trust, relevance nor authority to websites, they assign those values to individual web pages. A new page can be ranked on a new website just as easily as a new page on an established website if you understand how search engines really work and take advantage of that knowledge.