Google takes time to index a website. Google needs your website URLs in sitemap for the indexing. If you don't create a sitemap, create sitemap first after those submit sitemap to google webmaster tools. After that submit your URL into search engine (https://www.google.com/webmasters/tools/submit-url) this will helps to index your website fast.
Share your new website link in different trusted sources, bookmark it. Once you do these all defiantly your site will be index within 24 hours.
First finish optimizing your sites Meta tag, Meta description, head tag, image and content and then social bookmark your site and go to pingler.com and ping it. This will make your site to index faster.
Initially, you need to create xml sitemap foryour website and submit that to google webmaster tool after that,you need to do on page seo to your website which means, adding of title, meta description and meta keywords to your website.By,doing all these things, your website will be get indexed in the search eninge soon.