Many thanks to @snaxolotyl and @ann-the-shut-in 

Screenshot from Season 1, Episode 1

The Date is May 11th, 2014 (or the same date a teaser release for Voltron Force airing in the Philippines was dropped.). NASA reports use the Month, Day, Year formatting. So it is safe to assume Lance is referring to May 11th, 2014.

However, it could be XX14 for the year, but we’re gonna use 2014 for arguments sake. The upcoming leap year would be 2016 in that universe. Shiro was born on a leap year. Shiro would be turning one of the following ages in 2016: 20, 24, or 28. This takes place in 2014, meaning he would be 18, 22, or 26. 26 places him outside of the 14-25 “safe zone” that the SDCC Video states. We can narrow his age to 18 or 22. Shiro was born either in 1992 or 1996.

18 puts him in the official “5 teenagers” range that every single printed source uses. That would make him 17 at Kerberos. In my opinion, this man here? Could easily be 17 or 18. Also, not our universe, so they might let a prodigy pilot an important mission especially with the recommendation of a respect officer/researcher (*coughSamHoltcough*).

There have been studies done on how PTSD and Trauma ages people faster. Also, we’re dealing with Space Magic (aka Quintessence), it is possible the aging was a result of that. Not to mention time dilation… But that is a tougher subject than most can handle. Long version short on that subject: Time can either move faster or slower depending on gravitational masses. Sure most documented cases are in tiny amounts. We’re mostly going with Space Magic and Trauma for the premature aging. 

But there you have it: Shiro is either 18 or 22. 

- Mod Shiro