Our son has a science degree from an excellent state university. He applied online for many many jobs, and never heard back. When he tried to contact people, they directed him to the online application process. He did this for months before finally allowing a family member to put in a good word for him at her place of employment. Result - full time job with benefits. He didn't want to use connections because he thought it was unfair. It's tough getting started, especially if you're not in a 'disadvantaged group'.
Two of my sons graduated from “good schools” (physics and CE degrees) and got fantastic jobs right off. One contracted for six figures before he even graduated. I’ve never seen that kind of money.
And we don’t have any connections I assure you!
Perhaps we are outliers I don’t know. But they have done fantastic, been headhunted - one’s a senior software engineer and one is a systems manager or something right now.
My first job that actually used my EE degree was found by hand delivering resumes in an industrial park. The company that hired me said they never advertised because they either hired someone that an existing employee referred, or someone from another company they met while conducting business. Probably many companies that operate that way, and they would only ever advertise if desperate, and need specific rare experience.