Google's indexing process is complicated, with many phases affecting each other.
To get them to index your website quickly, you need to make sure there are no roadblocks preventing Google from indexing in the first place.
Secondly, do whatever you can to notify Google that you have fresh content and want your website to be indexed. Bear in mind that the quality of your content, and the lack of internal links may a deal-breaker in the indexing process.
Finally, boost your website's popularity by building external links to your website and getting people to talk about your content on social media.