Hello,
While you cannot directly link your Facebook page to a Google Ads campaign, you can use your Facebook page's content, such as images, videos, or posts, in your Google Ads campaign to create a cohesive marketing strategy across platforms.
You can use Campaign Google Display to promote and drive traffic your Facebook Page.
But please keep in mind, this suggestion based on my personal experience.
Since Google cant capture more data from your Facebook Page, so you only can use traffic objective in your Google Display Campaign and redirect it to Facebook Page.
Thanks