Well, there is a whole lot to this. Your first step is letting google know about the website.
This is done via registering with the search console and submitting a sitemap. ( this isn't needed but speeds up the process provided you have decent content. )
The second part is traffic. I've noticed when a website gets traffic to be it from social media, direct brand searched, marketing emails and you have decent user metrics Google will crawl that website much faster.
The third part is creating content that gets you backlinks, websites with authoritative content tend to get snapped up quicker by googles crawlers.
Some tips. Make sure you have no broken links and that your website is fast and does not cause a high server load. This may result in Google delaying the crawl. Google has a crawl budget and these things eat at it. Eliminate duplicate or similar content, again you are wasting google time and that's bad for your crawl budget. If you qualify get a Google my business account, a website with google my business accounts generally seem to get better crawling than those without.
Most importantly give Google content that makes it say wow we don't have anything this good we want it on our Search engine.