A common (perhaps the most common) way that self-taught persons are able to substantiate their self-learning to employers is through a portfolio (e.g. see this question). For example, a self-taught software developer can develop a software portfolio, or a self-taught journalist can build a portfolio of articles.
How can someone who is self-taught in a field that is not conducive to building a portfolio make a convincing case of their self-taught skills? For example, if someone has self-studied the skills of a Power Plant Safety Inspector (e.g. by reading books, reading case studies, etc.), it would be difficult (if not impossible) for them to build a portfolio of safety inspection reports without risking getting arrested for trespassing inside power plants or at least getting escorted off the property and threatened. Similarly, someone who has taught themselves the skillset of a Warehouse Shift Supervisor through some combination of innate talent, perseverance, and literacy might not actually have the resources to set up a sufficiently realistic warehouse shift simulator to build up a convincing portfolio of simulated supervisory shift interventions.
One possible way could be to pass some sort of certification exam, but many certifications now require substantial documentable formal experience and/or education that a self-taught person may not have.
For the purposes of this question, we are talking about a person who truly does have the skills (albeit self-taught), not an incompetent person who thinks he can do it but actually can't.
The question Effectively adding “Self-taught” skills on your Resume isn't actually what I am looking for because it is about the software industry specifically (one that is conducive to portfolio building) and the answer provided is more or less "get experience" or "build a portfolio", and I am asking about situations where neither of those are realistic. The question How to approach a company looking for a job self-taught, without formal qualifications? is also about software jobs specifically.