I submitted a paper to a journal one week ago. What does "Awaiting ME Processing" mean?
The acronym ME most likely stands for "Managing Editor" or "Manuscript Editor", and so the message says that the paper is awaiting processing by this person.  As shown in this question on the process for journals, that initial "processing" step usually involves an initial assessment by that initial editor, and if it passes that hurdle it will then be sent out for peer review by referees.