"We're going to constantly search for ways that good will come out of this," Granger said in a video posted to the family's YouTube channel. "That's my commitment to River's legacy."
Earlier this month, Smith announced on Instagram that 3-year-old River Kelly Smith had died after a drowning accident. In the new video, Granger recalled the playful mood of that spring day.
"I was outside, playing with London. We were doing gymnastics in the yard, and the boys were playing water gun fight," he said. "And I remember thinking -- I was looking at London as she was doing gymnastics -- and I thought, 'Soak up this moment' -- I just had this thought -- 'Soak up this moment because it's not going to last forever.'"
Granger said that just moments later, he and Amber were inside their pool gate doing CPR on River.
Reflecting on the tragedy, Granger said that he does not believe his son was taken too soon.
"We believe in our belief that God gave us River for three years and that was his mission, and I don't believe that God takes anyone too soon," he said.
Instead, Granger chooses to focus on how much living River packed into his short years, pointing out that his son had lived out his days -- approximately 1,000 of them -- as an example of how they should move forward.
"What if we all were given 1,000 days? What if you were given a gift of 1,000 days on this Earth?" he said. "And you could live those days barefoot, red hair flying back on your go-cart, on your tractor, full speed ahead? If you could do that with your family around, with no cares in the world? That's a good 1,000 days. That's a good way to live."
In honor of their son, the couple is selling T-shirts for which 100% of the proceeds are going to the Dell Children's Medical Center. So far they said they have raised more than $100,000.
The family is also raising awareness of a message in honor of River.
"Love those close to you," Granger said. "Soak up those moments. Live for today. Live in the present. Because we're not guaranteed tomorrow."
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PREVIOUS COVERAGE: Granger Smith's son, 3, dies in drowning accident
The Associated Press contributed to this story.