What is the best route to being a biomedical engineer?

I can either major in biomedical engineer as an undergrad, and then get a masters in biomedical engineering too, or I can major in mechanical engineering as an undergrad, and then get a masters in biomedical engineering.

I'm definitely more interested in biomedical engineering than mechanical and would probably have more fun studying it for undergrad, but I know that biomedical engineering is a much smaller field, and I've heard some employers would prefer to hire mechanical engineers even for biomedical engineering positions, because they think biomedical engineering is too broad.

Which route should I take to increase my chances of being able to find a job working in the biomedical industry when I graduate?

thanks