There are two ways you can try:
A very useful method of speeding up indexing is to get as many inbound links from quality Websites as possible. If you know someone who runs a popular Website ask them for a link and a bit of a plug, and don't forget to reciprocate the favour.
It seems that the more popular a Website is, the more indexing attention it gets from Google, therefore creating a good inbound linking strategy is essential.
Spend time writing interesting and useful articles for your new Website and these should start attracting more and more good quality links over time. If you don't want to manage your Website yourself, then we can as part of your package.
Of course, there is another way to drive traffic (visitors) to your Website. Don't wait in the hope of people searching for it. Simply advertise it!