TBH, some answers you will get are insane.
Some facts:
1. You can rank a KW within a few days.
2. You can rank a KW within several months.
3. You may not rank a KW at all.
It all depends on:
1. Competition
2. On Page
3. Link Building
4. How long you want the site to last
Some guys can get a domain ranking in about a week if they prepped the domain properly. Does it rank long term? Not usually. But it depends on the results you want. People who say you cant rank fast need to keep trying new things out.
Take an aged domain with a good and clean back link profile. Throw a long tail or very easy KW on the domain. Point a couple high TF/PBN links at it for indexing. Watch it rank fairly quickly.
Target a medium competition KW on a new domain and watch it not rank for three months.
It is all about context and a lot of variables.