Piece count by age is roughly right, and misses the thing that decides whether a child finishes: the picture.
The usual advice is to match piece count to age, which is roughly right and misses the thing that actually determines whether a child finishes a puzzle or walks away from it: the picture.
Guidance rather than rules — children vary enormously, and a child who has done a lot of puzzles will be a year or two ahead of this:
The right count is one where the child finishes. A puzzle abandoned at two-thirds teaches that puzzles are for other people; one finished slightly too easily teaches that they are worth starting. Err low, and go up when they ask.
Adults can grind through a difficult region because they know it will end. Children cannot, and will not. So choose an image with strong colour and clear separation, and avoid uniform areas entirely — a 24-piece puzzle with a plain background can be genuinely harder for a four-year-old than a 48-piece one of something busy.
Animals work well for exactly this reason: fur and feathers give almost every piece its own texture, and children recognise the subject instantly, which keeps them oriented. Food and flowers are strong for the same reason. Skip landscapes until they are older — the sky is where the trouble is.
A grandparent and a grandchild can solve the same puzzle at the same time from different houses, seeing each other's pieces move. There is nothing to install and neither of them needs an account — one shared link puts both of them on the same table. For a lot of families this turns out to be the whole point of the site.
You can also use your own photograph, which for a small child is often more compelling than any stock picture: their own dog, at 20 pieces, is a better first puzzle than anything you can buy.