Apply anyway. There are plenty of CRC and CTA employers willing to give you a shot as long as you have a Bachelor's of Science and some basic experience in school volunteering or working in a medical job on the side.
This is the biggest catch-22 out there. Even entry level job postings will want you to have experience. After a few years as a CRC you'll encounter the same thing when you want to be a CRA... Then after 5-10 years of being a CRA, you'll encounter the same thing when you want to be a clinical trial manager and then again if you want to go into project management or into being an executive. You just need to find someone willing to give you a chance and make good connections.