How can I determine if I will be approved for EFMP for Camp Vilseck, Germany?

Only EFMP can tell you if you'll be approved for EFMP. Anything anyone says here is speculation with a dash of BS. The more certain anyone sounds about whether or not you'll be approved, the more full of BS their advice is.

Start the command sponsorship process now, if you're denied you can apply to have your orders deleted, wait too long and you'll be alone in Germany for several years.

Seriously, anything anyone else says is complete bullshit. I'm a Career Counselor, I've reenlisted at least hundreds of people to go to Germany and OCONUS and I can't tell you when EFMP will approve or deny command sponsorship. EFMP can't tell you reliably if they'll approve or deny command sponsorship.

The best thing to do is contact the EFMP Program Manager in Germany. As SFC Boyd says, only EFMP can tell you if you will be approved. Currently the EFMP folks are located in Weisbaden. You can email them at this link.
https://www.armymwr.com/location-contact?location_form_location=68934

If you want their physical address and contact numbers, here is their information.
Clay Kaserne
Flugplatz Erbenheim
BLDG 1201, Room 113
Wiesbaden 65205
Germany
+49 (0)61 [login to see]
DSN [login to see]