No Experience - No Job - No Experience - Vicious Circle

I've just discovered a new kind of "perpetual motion machine": a job candidate (it's me) that cannot get a job without experience and cannot get required experience without a relevant job.

Today, I've received an automated rejection email specifying my lack of healthcare industry experience as a main reason for rejection of my attempt to get into this new for me industry. 

Right now, more and more big Healthcare companies are expanding their business of claims processing in Phoenix AZ. 

Every day, I find tons of new Data Analyst openings ads in Indeed and 
I am applying only for 1-3 most matching.