It's like anything else, you can be told it can't be done, and then there is that one person who is willing to give you a shot. But it isn't a generally available thing. Also I know a guy, I tease him as being a skills leech. Back when we were coming up in the 80s, this guy could move anywhere and get taken on by anyone. He would just stick to whoever he thought would be able to help him along, and people helped him. Unfortunately that was his great gift. He wasn't gifted in any particular thing he took up... Unfortunately for a lot of people, getting people to reach out to you can be for reasons you don't want.
The problem with the unpaid stuff is people think that giving of their valuable time is a gift to the people they want to work for, as it can be. But a lot of small business people find the months where their staff are learning, even if unpaid, are very very costly to their businesses. The person doing the learning feels they are paying for it by donating time, or working for low wages. They then leave after the learning is over, at just the time when the repayment would be starting to happen. I just mention it because knowing a bit about the economics is key to inserting yourself. People often don't want to help because they assume the person coming to them doesn't understand the costs to them, and it is just easier to say no from the outset. So the trick is to get creative about it from the outset. Since I like the whole self-taught part about crafts, I don't really know the answer, but it could be trading something you already know for the exposure, rather than trying to get taken on as an apprentice. Give tax advice or work in reception!