I've been wracking my brain, and I can't come up with any possibilities that haven't been mentioned.
Either Maria was given to them, bought by them, found by them as an orphan or abducted by them. There really aren't any other options, since we know that she wasn't born to them. I do know that if a Roma woman were going to abandon her child, she would be likely to do it within the Roma community. They are very distrustful and pretty secular.
Two things that I really do believe the Roma wouldn't do, is steal children (at least on an organized level) or sell their children. I am not talking about accepting a dowry when they are married off, that, to me, is simply a cultural difference, and I'm not going there. Selling a child, for the majority of traditional Roma families, is the equivalent of selling a house for one month's rent, instead of charging the rent over and over again. (This, I see as a side effect of the abject poverty most communities live in. They love their children, but they see the financial opportunity in everything. For girls, stealing or begging and then finding a husband are rites of passage, and while most girls do stay out of prostitution, because they are more valuable at the time they are married, but if they don't find a husband, or if they do and are poor enough, prostitution is all that's left. So, yes, children are valuable, well into their thirties, because in Roma communities, a family is not two or three generations consisting of 10 people, some families are three generations (or even four) and that one family may number as high as fifty. All living together or within very close range. They may be travelers, but they travel together. So, if anyone in the family is bringing in money, it benefits the whole family.
This also explains where the money goes. Imagine this. You, your parents, grandparents, three aunts, four uncles, seven children, 8 siblings, 17 cousins, husband, and 14 members of his family, are all dependent on one communal income. But not everyone contributes. Some of the family are too old to work. Some may be injured, or too young. Some may drink every penny they do make, plus more. It is the unwillingness to split into smaller family groups that often drags them all down.
That said, Roma families do not trust the police, or outsiders. Especially police. While they do steal, and they do prostitute themselves, these are both things that have been handed down through generations. The stealing and begging is taught even before the fear of the police, and these are both crimes that are right now, committed in the moment, and then they can run. They are not involved crimes like kidnapping, which require planning, and carry a serious risk of bringing a lot of unwanted attention for outsiders.
That said, I do believe that someone gave her to them, or they bought her, but it would have had to have been a significant amount of money that they paid. I don't believe they simply found her wandering. I also don't think that her parents will ever come forward. But if they work backwards, and find out where this family was, every step of the way, and find and talk to every single person that had contact at with them, they may be able to figure out where she did come from and exactly when. Children do not just appear. Even among Roma, there would be questions asked. Especially by those that truly fear police and outsiders, instead of just being very distrustful of them. Kidnapping is not the norm for their society, someone would have noticed.