How long exactly does it usually take before a site starts getting organic traffic?

[smartscraper]

Generally in a month you can see the traffic coming to your website.

[jahnvi arora]

One important thing to remember is that organic search engine ranking only happens sometimes; it can take several weeks or even months for your site's rankings to improve dramatically. If you're consistently publishing high-quality content and doing your best to promote your site, you're likely to see some results sooner rather than later. Organic traffic grows more slowly than SEO-driven traffic but eventually catches up.

[charlesprabhu]

It typically takes 4-6 months to see organic traffic from SEO