The administrator rights for Confluence cloud are two layers. You won't get the higher layer, that's reserved for Atlassian support, but the application admin right is controlled by "global permissions" - that names a group, or set of groups for admins. If a user is in one of those groups, they have application admin rights. So look in there, and then add the user you want to have admin in there. You can then get them to remove you (you said change in the question, so I assume that's the end goal)
Milo gave you the answer for Space administrator
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