Submit a sitemap.xml via Search Console.
Generate a link from a site that is currently indexed to point to your home page. This usually speeds up the indexing process.
Be aware, there is an API that people talk about using, however, this is only designed to be used by publishing sites (news sites) and is not designed for normal public use. There is an outside discussion/threat that normal sites that use it could face backlash.
To be safe, upload a sitemap.xml and you should be indexed within a few days for a brand-new site. If you have an existing site and post regular content, you can be indexed as quickly as 15 minutes - just depends on the type of site/content you run.