The following method will work. I've done it myself, and would hire anyone that used it with me. You will be the only person the company is looking to hire, if you follow this idea. Ready?
About 30 years ago, I decided to open a retail store. I wanted to learn how to do that from someone respected in the business I chose. So I asked several people (in the retail vacuum cleaner business) who they thought could teach me. They all said one thing "Whatever you do, don't go see Julius Toth. That guy is evil"
So now...I had to meet him.
I walked into his store, asked to talk to him, and told him that I wanted to work for him. He said "I have 5 guys working the floor. I have no openings. Sorry"
And here is what I said;
"I want to open a store like yours. You are the guy I want to learn from.
I'll make you a deal..pay me whatever you want..straight commission, small salary, nothing...I don't care. I'm here to learn from you.
I'll work with you for 6 months however you want to do it. I won't take any sales away from your employees. I'll make you money. I just want to learn how to do what you do"
He sat back in his chair for a minute. I knew I would get what I came for. He had nothing to lose and everything to gain.
He said "Ok. I'll pay you a commission on what you sell. And I'll teach you everything you need to know. Just agree that you will open a store at least 25 miles away". "Done" I said.
He ended up giving me a very generous pay. In the early 1980's I was averaging between $800-$1,200 a week. It took me a week or so to figure out how I was going to make sales without taking sales away from his other guys..but it worked out fine. I worked about 4 hours a day, and learned everything I needed to know to start my own store. He even gave me starting inventory on consignment. We became fast friends even till today.
So...I know what you are thinking "I don't want to work on commission" "I don't want a retail store" "I don't want to sell anything" None of that matters.
Here's what matters; I said I wanted to learn his business, and I wanted to learn from him. I didn't care what I was paid, because I was learning while I worked with him. I wouldn't cost any money, because I'd make sure he made money on me. (You can say that even in a salaried office position).
And why does this work? Because employers never hear it.
At my store, I get, about every few days...someone poking their head in the door "Are you guys hiring?" "Are you guys taking applications?"
The answer is always a swift "No".
If someone would walk in and say "I want to learn this business, and I've been asking several other retailers, and they say you're the guy to learn from. Pay me whatever you want. I just want to learn from you and make you money."
...I would hire them in a heartbeat.. I may even adopt them.
Why? Because now it's about me, and what he can do for me...not about what I can do for him. And nobody...nobody ever says what I just said.
If you were one of a thousand applicants...you would get the job. You would be so unique. And you would be unique in a way that is attractive to an employer.
I know this would work with small businesses. Large companies with HR departments? You need to talk to the person that owns the business, or the CEO.
Go get em.