Is there a way to recursively get all FieldDescriptors in protobuf?

Question

I am trying to implement a way to check if all nontrivial fields in proto3 message are set (since presence is not encoded for trivial types like int).

I have code like this

namespace pb = google::protobuf;
bool HasAll(const pb::Message& msg)
{
    std::vector<const pb::FieldDescriptor*> fieldDescriptors;
    const auto* reflection = msg.GetReflection();
    reflection->ListFields(msg, &fieldDescriptors);
    const auto* descriptor = msg.GetDescriptor();
    const auto numFields = descriptor->field_count();
    const bool same = numFields == fieldDescriptors.size();
    return same; 
}

This seems to work at "top level", but I wonder if there is a way to tell the reflection and descriptor to recourse into submessages, so my fieldDescriptors contains the data about nested fields, and numFields also counts the fields in nested fields.

I know I can manually implement recursion, but I am hoping somebody already solved this problem.

note: I know in general why fields are optional in pb3, long story, but I really really do need all fields to be set.