How to recover the penalized google website

If you really want to try to solve this (it is not recommended, as other people said) you would first have to do an audit of the website, both on the page and on the SEO page.

You should first check the seoby page using tools such as Screaming Frog to identify, duplicate content, redirect URL, structure of the website …

Also, visit mannyaly through the website and look for warning signs, poor quality content, affiliate links, ads (if applicable) and anything else that seems unnatural and of low quality.

Tools like Ahrefs or Semrush give you a perspective of a backlink profile. If it was heavily spam with low quality links. You could reject those low quality links through the Google webmaster console.

After fixing all those (a lot of work), I would have to restructure and improve the content of a website.