Can we add an Office 365 dynamic group inside SharePoint site permissions?

Dynamic groups are basically created to automatically include / exclude users into a group who meet a criteria like Department, Office Location etc., So, the group is managed automatically, so as users meet the dynamic criteria, they will be granted access or removed from the SharePoint site accordingly. Important points to consider

Permissions Inheritance: If the site permissions are inherited from a parent site, you may need to break inheritance first to modify the permissions at the site level.

Permissions Sync: Changes to the dynamic group (e.g., a member added or removed) will be reflected in the SharePoint site permissions, but it may not reflect immediately.

See if this guide helps. 

https://blog.atwork.at/post/Dynamic-groups-accessing-SharePoint-Online