I can't think of any particular 'pre-tech writing career' types of jobs. In my case, I got my first tech writing job at a company I'd been working at for six years. I volunteered to do any writing and design tasks in my previous positions (which were mostly clerical and data entry way back then), even though the tasks weren't part of my job description.
I was promoted to the tech writing department from within the company, and then had several subsequent tech writing jobs before I ever got my degree, but that was a decade and a half ago. In an employer's market like now, whether a candidate has a degree is often the first cut when HR is reviewing resumes/CVs. It's not always fair (in my first tech writing job, the best writers in the department were also those who didn't have degrees), but it's reality.
So, as far as getting experience, many types of corporate jobs might provide an opportunity for you to get some practice. For example, if you have programming skills and have/get a job as a programmer, you might be able to write source material for the tech writer on a project, and then work closely with the tech writer during review so as to pick their brain and learn new stuff. Maybe you could get a job as a copywriter for a catalogue company, where you'd be writing and could learn some layout. You could volunteer to write, edit, and/or lay out white papers for the company you work for. If the department you work in (literally ANY sort of job) doesn't have a 'policies and procedures manual', volunteer to write one; if it does, review it to see if it needs to be updated, and if so, volunteer to do the work.
Written communication is key to any company's business practices. If you can't find a job where 'writing' is in the job description, there still might be lots of opportunities for you to take on extra writing-related tasks.
Good luck!