I think your best best would be looking at local businesses rather than large chains. AFAIK, all supermarkets require a C in maths now. A local cafe or pub, on the other hand, might be willing to give her a chance if she goes in and presents herself as keen and enthusiastic.
I think you would be surprised, depending on area obviously.
Start by volunteering in a charity shop, then try washing up in a pub or hotel with that reference. Progress to waiting and bar work.
Not unreasonable that the right person could end up in a managerial role. DH has often employed people on this basis. One person in particular with no qualifications at all was offered a share in the business after 10 years.
Contact the Virtual School for the authority she is in care to- they should have local connections with organisations which prioritise children in care and offer positions which take account of lack of qualifications/experience etc.
At 17 she would do well to become an apprentice which would also get her sorted out for maths and English. Try googling training providers and local colleges. There are apprenticeships in many fields including retail, hairdressing, childcare etc. She will just need to be presentable, puctual and willing to learn.
Unless i live in a paralell universe, lots of supermarkets will take on 17 year olds without qualifications. Aldis do tend to pay more and are less likely to take on without experience. If she walks along the high street and looks in thd windows there mat well be part time staff needed
I hire for apprenticeships in an office environment but still need GCSE English and maths plus interview. Looking for an understanding of responsibility of work, respect for other people, proactivity and problem solving skills. So not experience as such but strong personal skills instead.
Does she have these? Or examples she could use/feel comfortable talking about in an interview?