I just landed a full time position as a 2D Motion Designer and Illustrator for a agency that mostly focuses on education and school based content after about a month of searching/interviewing. The positions can definitely be a bit rare depending on where you live, or have a ton of applicants if they are remote (I'm working remotely), but they are out there. Like others have said, having a portfolio full of the work you want to do definitely helps get your foot in the door.

Also be careful during your eagerness of where you decide to work. I've been bait and switched in the past on workloads and descriptions (Like my last job doing a 180 from being Design and Animation based to wanting a videographer/photographers skillset)