This isn’t a one-answer-fits-all. The outreach process has many steps and the biggest variable is the authority level of the site you are hoping to build the link with.
Lower authority links can be turned around within 1 month from beginning to end.
High authority links can take longer due to forming a good relationship with site owners and the negotiations on topics etc. However, building high authority links is often worth the additional time needed as they offer a much higher SEO return.