Career guidance in doing a transition from automation engineering to data science

I do have a double major in electrical engineering and applied statistics but I am working as an automation engineer at present. I would pretty much like to change my career path into data science. But most of the interviews I face and opportunities I get would get mostly rejected as I have no experience in working with analytics. What is the best way for me to do a career transition and convince the recruiters on how my career transition is valid and worthwhile.