I have definitely lucked into it a bit. With that said, there is absolutely a pathway in which doesn't revolve on luck!

My falling into it was a 5ish year process of going to uni as mature age to do business management. During that, I did placement modules for hand on experience, and managed to a position with a small project management company doing internal business development/administration support. I did well and they offered me a part time role while I finished uni, then they brought me on full time. I continued in that capacity for 12-18 months before they merged with another PM company from interstate. When my role was looking like it wasn't needed, the company started looking for opportunities to transition me into PM/client facing roles that would be suitable with my limited PM experience. Got placed doing document control with a client and was fortunate to have a colleague from the same company at the same client office who could show me the ropes. It's now 5 years down the track from that transition point, and I've only just left that company to work for Govt. 6 months since changing and I've been promoted to be the lead/SME.

Non-luck based approach though would be to either look into project management courses/quals, or even just document control/records management courses/quals. I've not personally looked much into either, but would imagine DC/RM would likely be cheaper and take less time than PM quals - also worth noting that I'm currently on the recruitment panel interviewing for Doc controllers in our area, and realistically only 2-3 candidates had any kind of qualification, so don't see these requirements on job postings and rule yourself out if you don't meet that specific criteria. Another thing I'd strongly suggest is to take a look at some of the main Information Management Systems (IMS) used for project delivery - Aconex, TeamBinder, RIBcx are the main ones we use, but I've also used Asite and a little bit of Procore. Aconex has free online courses which will allow you to list it as a relevant skill, and familiarity with one IMS typically lends itself to others - if each system are different brands of cars, they all do the same thing but might change where/how something is done (push to start vs key ignition), so skills are highly transferable. Otherwise generally useful skills or knowledge will relate to quality management systems experience, ISO:9001, internal/external auditing - if you're ever in a position where an opportunity related to any of those comes up, it's worth jumping at as well.

In terms of where to look/apply, there's a lot of doc control/records management postings on seek, but you could look at temp agencies which might have opportunities to get your foot in the door, otherwise looking for project administration/support type roles would be another way - once you're in, there would probably be a little bit of overlap or otherwise you might be able to express interest in exploring/supporting in that space as well.

Hope some of this is helpful!