Is it possible to match the people that liked our page with contacts in the CRM?

Is it possible to match the people that liked our page with contacts in the CRM?

Hello!

I would like to connect our contacts in the CRM with their profiles in Facebook. How can we achieve this? Is there a way to do it through the likes in our Facebook page? So far, I have been only able to match with contacts or leads that sent us a direct message via facebook. Most of our contacts do not contact us that way but then they go and like our page.

Is there a way I can do this?

I would like to have their social media profile picture in the CRM contacts picture.

Best regards,