The following is the FAQ link for all questions related to ocmjea :
https://education.oracle.com/pls/web_prod-plq-dad/db_pages.getpage?page_id=451#3a
Please refer to the Assignment and Essay section for all your queries
According to Oracle,
"Candidates must have a submitted assignment on file before they are able to register for an essay appointment with Pearson VUE. Once you have submitted your assignment, you will be able to schedule your essay appointment."
But there are candidates on this forum who have given the essay exam first and then submitted their assignment. Please refer to this link :
https://coderanch.com/t/500959/java-Architect-SCEA/certification/Tips-do-expect-after-Part
But this was in June 2010 which was more than an year ago.
Hope this helps.
-SP