Officials Suspect Food Poisoning Played Role in Brett Gardner's Son's Death

12:15 PM PT -- The Arenas Del Mar tells TMZ Sports the Gardners did not eat at any of its restaurants for lunch or dinner the day before Miller's death ... but will continue to work with the family and officials on the tragic matter.

It also noted the establishment had an inspection on March 14 ... and received a passing 98.5 out of 100 score.

The cause of Brett Gardner's son's sudden death remains a mystery ... but Costa Rican officials said Tuesday they believe food poisoning might have played a role in the tragedy.

14-year-old Miller Gardner passed away Friday while on vacation with Brett and other family members in Manual Antonio ... and, initially, investigators thought he might have died from asphyxia, as his body was found with vomit on it.

But Costa Rica's Judicial Investigation Police told CNN on Tuesday that after they discovered the teen's airways were clear, they now believe his body's unfortunate reaction to a meal was what sparked the passing.

CNN reports authorities are awaiting toxicology results to make the official determination.

Brett and his wife, Jessica, stated on Sunday they had "so many questions and so few answers" ... though they did reveal Miller and other family members had all fallen ill at around the same time while on their vacation.

"Miller was a beloved son and brother and we cannot yet comprehend our life without his infectious smile," they added in a statement. "He loved football, baseball, golf, hunting, fishing, his family and his friends. He lived life to the fullest every single day."