What you described looks like a nested tree structure that you can probably display using a similar strategy to file explorers where you expand and collapse nodes to show or hide more details.
In this case, your nodes are not individual entities/items but progress indicators, which the node representing the overall progress of the individual child elements....
If users really want (and need) the loading details of child elements, show them when they ask for it.
If users aren't getting value out of more data in the majority of use cases, why not give them details on demand.
If there's no debugging needed to be done (which would be the case if a child component fails), let them click for more if they ask for it.
Is there a case where users need to know exactly the percentage for what's being loaded? I'd show just one progress bar indicator for the overall loading process and you could have a list of what's currently being loaded.
Child 1, Child 2
[======================42%-------------------------] 1 MINUTE LEFT
I'd suggest using a circular progress bar with the number / percentage written inside of it, this way you are giving your users a more accurate information, meanwhile also making sure it's still quick to scan. Something like this: