How can I land a job in Korea with an E-7 Visa as someone who doesn't have any yet?

I have just graduated with a bachelor's degree in my home country and want to work in Korea within the next few years. However, I'm struggling to understand the visa and job application process. I don't think I can get enough points for a D-10 visa, so I'm thinking of aiming for an E-7 instead, but I don't see a lot of companies offering sponsorship for that visa. If they do offer, they're looking for candidates who are already holders of other types of Korean visas and living in Korea. It seems like applying for and getting a job in Korea is impossible for those who don't have a student or D-10 visa. What can I do?