I agree to get children out of poverty you have to get the things directly to the children.
So yes free breakfast club, free school lunch and then after school with dinner / youth groups with food.
You could mix youth group with teaching them how to cook basic cheap food.
That way every child has access to three meals a day Monday-Friday. Youth group could still run Saturday and Sunday.
It could also be a discreet way to get clothes to children who are clearly in a need. Which are given via funding / donations. Someone comes in with holey shoes or a coat two sizes too small and quick check out the back/message to the place and something is sorted.
But this the has to be open to every single child even if their parent is a millionaire because you need to stigma.
During holidays you still run youth club and have basic food parcels no cash delivered opt in/out.
I know Amazon where delivering on behalf of someone as saw it popping up on the local facebook page various people where getting boxes delivered weekly with cereal/bagels/beans/uht milk/soups and all sorts of other long ish life foods.
Though this all costs money, but then again I’m sure people would rather taxes rise to provide this for all children than rise so Debbie with 6 kids and 5 baby daddies gets an extra couple hounded personally each month so smoke and drink up the wall.