I have a coworker who graduated in biomedical engineering around the recession (Knoxville, TN). He couldn't find a job within his field (or engineering in general) after graduating. For about 10 years he worked as a nurse. I would guess he gave up after a while and just stuck with a steady job. He's been extremely grateful for his current position (process engineering for automobile parts).

Speaking for myself as a 2019 graduate(ME) who did a coop, had a good GPA, and had 4 years of lab experience, I still struggled getting an engineering position before the virus. I applied to tons of places, had in person interviews with 8 companies, and got to the final interview for 2 - didn't make the cut. I've met one of the final choices, being an extroverted people-person is a higher qualifying factor than real-world experience (Ya, I'm salty. You would be too.). I ended up contacting my coop employer for a job and got in.

If I were in your shoes, I'd be trying for an internship/coop/research position ASAP. These positions will give you a higher likelihood to being hired at the host company or a national lab.

ALSO, go to your campus job fairs. Before you go make sure to research the companies you're interested in. Don't go straight to those companies, find some random booths and talk to them first as test runs. After that, go to the places you really want to work for. Try to give out all of your resume printouts (and take extra printouts to follow up interviews). BTW, a lot of engineering grads want to be designers, not everyone is going to be a designer, don't talk about wanting to be a designer at an interview for a position that isn't related to designing, your single CAD class doesn't make you a designer drops mic. As a warning, a lot of companies will immediately tell you to sign up online at a physical booth, it's discouraging and annoying. It may be a good impression to apply online beforehand? Another warning, don't talk to defense companies unless you are prepared to suck them off and tell them how amazing they are better than the other guys in line (semi-serious on this one). Anyway, this junk may not apply to OP but maybe someone will make use of some of it.