How much time it takes to recover the ranking after google Link spam algorithm update ?

While outreach is an effective way to recover from a link-based penalty, it isn't always necessary.

Links are one of the ways Google understands what content may be helpful to searchers, and they can be good for sites to receive,

There is no magic formula for ranking a website in Google neither there is anyone that can tell you how long it will take to get to the first pages. According to several studies, if you are starting a website now then you may have to wait for 3-4 months until you see your first visits from Google.