Having worked in volunteer coordination and being a volunteer in a few different roles for different organisations on top of my full time job I wonder what kind of volunteering your child's been going for? Nearly everyone who's applied and shown an interest has ended up with a role at each organisation - arts centres and theatres (front of house, box office assistant, gardening, maintenance assistant etc); food charities and community focused charities e.g. food bank, warm space; sports club (events, fundraising, coaching), church (gardening, cleaning, events) etc. And they've all included free training for volunteers (first aid, food hygiene, safeguarding, disability awareness etc).
I do get your frustration and it's great that she's got the Tesco job as I hear that it's harder to get part time jobs for young people these days.
It's hard to give specific career advice without knowing the sector and context. She's clearly bright and determined from her grades.
When visiting uni open days with my upper sixth son over the last couple of years, one thing that struck me as a difference between the russell group red bricks and the unis which were formerly tertiary colleges was their approach to industry connections. At the former, there was an assumption that you already had these networks and made connections with any placements yourself, at the latter there were deeper long-term tangible industry connections and they really showed off the link between placements and employment for students who didn't come from a background where they had existing industry connections. Privilege isn't just about money. It's one of the main reasons my son's chosen to do a degree apprenticeship so he's in industry from the get go but he still gets the qualifications he's capable of.
That's not helpful for you and your child other than to say it's not necessarily something she's doing wrong.
You're right that the Job Centre has very different priorities. In my sector I'm involved with projects which support early career entry level opportunities and could signpost.
My stepdaughter found it frustrating when she was looking pre 18 as there was an age limit on many opportunities but her career is now in the area she started work at on a part time basis. I think it helped that her work's been with smaller more local organisations rather than a big national beast as she's really been supported in her skill development.
I would personally be wary of the £500 thing. Do you have any testimonials from people you know who've done it? It could help her make connections, build her network etc. But maybe she'd get that from attending other industry related training.
Whoever suggested Chat GPT I say "eww". It's so flawed.
I can see you saying she's being turned down for call centre and cleaning jobs and you recognise that these won't necessarily help with routes into her industry of choice. In my recruitment experience in my sector, I'd say relevant experience is so much more important you're right.