Sounds to me like what you are asking for, and which seems a good idea alot of communities would benefit from, is a setting like data_explorer_allowed_groups which lets you provide full access to data explorer to more groups in addition to admins.
Presumably then if the group is allowed access, then the API key of that user would work to create queries as well as access them.
Currently it’s only possible to let people access existing queries, via their groups page.
I’ve moved this to Feature so the feature request can be considered. Not sure it will be picked up but this at least puts the idea out there.