You can start and create back links because it will increase your change of indexation.

You can also tell Google how often to crawl your site for updates, as well as many other useful tools for you to check your site's performance.

you have to good content

In Google webmaster tool, in dashboard click on Diagnostics then click on fetch as Googlebot, Type the URL to fetch or leave blank to fetch the homepage. by this way your site will index much quickly......

To Index a new site in google first create a sitemap if its wordpress or other cms and if sitemap is not possible create sitemap page and tell google about that page by pinging.

Without a sitemap, crawling can take a long time — as long as 24 hours to index a new blog post or website. With a sitemap, you can shave that time down to just a few minutes. That's right. Your website, blog, or new page can be indexed by Google in less than an hour.

How to Get Google to Index Your New Website & Blog Quickly - https://blog.kissmetrics.com/get-google-to-index/

you can simply search on google.

If you want to index your site, then you should create an account with Google Webmaster. Then, through Google console, you can submit your site URL for indexing.
Similarly, you can create an account with Bing Webmaster tool and submit your site URL there.
Another way is - use ping sites for indexing.
In case you want to know more about ping sites, you may visit https://hariforyou.com/ping-sites/

Submit a site map which helps Google to index your site quickly.

This is very simple to index any new website by search engines, submit your site in social bookmarking sites and ping the backlinks, it will work.