Crews have worked around the clock digging an intersecting tunnel to free the two-year-old boy, whose first name is Yulen.
His father, Jose Rosello, said the ordeal has been difficult but added he's feeling encouraged as rescuers inch closer.
"My wife is broken ... we are dead inside," Rosello told reporters on Wednesday. "But we hope we have an angel to get my son out of there."
The well is located in Totalán, a town in the southern province of Málaga.
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It is about 360 feet deep and only 10 inches wide.
A few hairs found in the soil extracted from the well during the rescue operation provided DNA matching the boy's, said Maria Galvez, a government official at the site on Wednesday. That confirms that he's inside, she added.
An attempt to send down a robotic camera on Monday was only partially successful. The device made it only 229 feet below the surface when the hole became too narrow for it to go further. However, it managed to spot candies Yulen had been carrying.
Efforts were made to widen the well but hard rock has impeded machinery from getting past the 262-foot mark, according to Galvez.
The country's air force transported a mining rescue team to the town to support crews already at the site.
The specialists were on site Wednesday aiding in the dig of an intersecting tunnel, which has to be executed carefully to prevent an internal collapse within the well.
Galvez said that crews expect to reach the deepest portion of the well by Friday.
"Now they are making progress ... we have a bit more hope," the boy's father said.