[I have a fairly new site, approximately 2 weeks old. When I type in my target keywords, I can’t find my site on Google. When I type in my longtail domain name, it shows up #1. For example, “dog training”, I can’t find my site on any Google page. For “dog training HQ”, it shows up #1. Has my site been sandboxed? Is it the google dance? The only reason I can think my site may have been penalized is too much keyword stuffing, in the sense that I used my keyword too many times throughout my site (not hidden somewhere).]
It sounds like you are expecting your brand new pages to outrank millions of other pages that have been optimized for your targeted keyword. Why do you think you deserve to be ranked so high?
One of the factors in the ranking is trust. Your pages are too new to have earned much trust on their own. Start getting relevant backlinks from pages with a good reputation. As you promote your pages with those backlinks your own reputation, and trust, will grow and help to earn higher rankings for your pages.