It does take a bit of time because the search engines have to find your website first in order to index it for search results.Submitting it to Google as the other person said, will help. You can also add the link to your website to Twitter and, once posted, it can help bring the search engines around a little sooner than otherwise, to find and index your site.
In order to rank higher than other sites in the search engines, you will have to have good on-page SEO (the meta tags you referred to), good website interlinking structure and some off-page SEO. The off-page SEO is links and activity (social signals) on sites like Facebook, Twitter and Pinterest, and links from other relevant and somewhat relevant sites related to daycares, children, parenting and that sort of thing.
You can visit other websites and blogs that are related and leave comments on their blog posts. Make them relevant comments to the post. Many of these will allow you to leave a link back to your site.
Get a link to your website (inner pages, as well as home page) on other local community websites where you can.
All of these things will help your website be found and indexed by the search engines and help you move up a little in the rankings. Keep up with your SEO and with adding new content to your website each month.
Be sure that you have also gone to your Google Local Listing on Google Plus and 'claimed' your listing. Add your business hours, location, etc and some images and video. This will also greatly help your rankings locally and definitely getting indexed with Google.
Hope that helps. All the best with your site.