His desperate mother Sabrina Benitez believes her son was abducted - insisting that it would have been impossible for him to get out or that he would have been smart enough to try to get back in to their New Braunfels home.
But cops have refused to issue an Amber Alert because they say it's unclear that he was abducted.
Holding back the tears Sabrina, who is expecting her fourth child at the end of the month, told KVUE: "I know just to see us on TV would make him happy. I love you, and I can't wait till you're back home."
She was watching "Toy Story" with the toddler shortly before 8 p.m. Friday when he left the room, heading toward where six other adults and another child were.
About 10 minutes later, when the boy hadn't come back to watch the video or pick up a toy, Benitez asked the others about his whereabouts.
A frantic search ensued, but when they couldn't find him, 20 minutes later they called the cops.
But New Braunfels Police Lt. Michael Penshorn said as of Monday, it's most likely that young Joshua Davis Jr. left the home without anyone noticing or taking him.
He said: "The first scenario that we are looking at is that somehow the child was able to exit the house and basically disappear into the night."
No Amber Alert has been issued for Joshua because such an alert typically requires solid evidence that an abduction took place.
Police searches involving people, helicopters and dogs along with the help of hundreds of volunteers have as yet to locate the boy.