You have to meet the physical presence test requirements before you can file the exclusion. Then you can pro-rate your total foreign earned income exclusion between 2016 and 2017.
In your situation, you must be physically present in a South Korea for at least 330 full days during the 12-month period starting June 2016. You have to wait until after July 2017 to file your 2016 return to make yourself eligible.
Here are your two options :
1. You can file Form 2350 for an extension to file your 2016 tax return.
See https://www.irs.gov/uac/about-form-2350 OR
2. File your return timely without claiming the exclusion and then file an amendment return after July 2017.
[Edited 1/31/2017]
