I believe that with the "new" application (it's been online for months) you must meet all the criteria before you can apply; so yes you must have an FE written first (it'll ask when you took it).
Also, you cannot update your resume you sent in prior to the new format because it is no longer on file; everyone who'd applied in the past had to reapply with the new application. In the past you could apply with just 100 hours of multi-engine time but now the system will reject all applications that do not meet the minimums. Get the written ASAP and try again, they'll be hiring hundreds of pilots next year, have heard 300, I also have heard 600, so who knows. Good luck!