There's no set time for when your website will be crawled by google. But you should have your website crawled and indexed by 3 months at the latest.
Google also keeps new websites in what they call a sandbox to let them mature for around 6 months.
So even if your website was indexed by google right now you're likely to not get any search traffic for at least 6 months.
Ranking in google can take from 3 to 6 months as well. But older websites can rank a new post within 1 month and even 30 minutes.