Is it possible to do programmatic automation with Final Cut Pro?
Davinci Resolve and Fusion would be a better choice than FCPX/Motion if you're looking for something that supports standard scripting languages (lua and python 2/3).  From there, you can install whatever modules you need to get hooks into your data.  Adobe has their own ExtendScript for AfterEffects, which is based on JavaScript, but I can't really comment on it.  FCPX and Motion are probably the least script friendly of the major NLEs.  I'd guess that most larger studios probably use Nuke, which also uses Python, but if you're just starting out, Resolve/Fusion is a cheap entry point which scales well towards Nuke.

Automation of large file sets typically falls under the purview of a production's Technical Director (TD), who would be great people to befriend if this type of work interests you.