Is it permissible to create a website for the Holy Quran (audio) that generates profits from Google AdSense advertisements, which are then allocated to charitable work, bearing in mind that AdSense policies permit advertisements for non-Islamic websites or those containing immodest images, and that control over the advertising content is limited?

It is a condition for the permissibility of accepting advertisements that the website owner must be able to control what is published on their page through filtering or screening. If they cannot control the advertisements, then it is not permissible, because a person is responsible for their page and what is displayed on it. A good intention behind advertisements, such as donating profits to the needy, does not make the unlawful permissible.