Hmm. I don't agree with you. My degree is chemistry from a good-not-great institution. Since getting into SE, I've progressed to technical leadership very rapidly.
I have dedicated myself to applying for jobs, but it's not that much work. It's about making sure you advertise matching strengths.
I make sure my CV only has the minimum information needed to sell this. Then only job of my CV is to get a callback. After that, it comes down to my interviewing.
I also have an extraordinarily high success rate. I've applied to 8 SE jobs in my career. 7 of those led to interviews, 4 to jobs. Of the three interviews, 2 of them I chose not to progress with (i.e. they didn't reject me, I rejected them).
Maybe my strength has been applying to realistic opportunities. My first jobs were low paying roles in non-tech companies.
Remember that your strongest selling point is your most recent experience. As a fresh graduate, your university matters the most. As soon as you have your first job, your experience here will dictate your next step.
Since my first job, I still get asked about how I transitioned from chemistry to SE, but the tone has changed. People don't expect me to justify the change, they want to hear about the similarities, differences, and strengths that have translated. It's become one of my favorite interview questions to answer now.