Not necessarily so. In fact, I think the bulk of them were sent by their parents, who remain in El Salvador, Honduras, etc. (about 80% are from Central America, as I understand it).
It could be a combination of both of course. But you have pointed to an even more sinister plan, in that they send the children first, and then the humanitarian cry by the left is that the children MUST be reunited with their parents. And then, the parents will be allowed in to this country.
“Sent by their parents...”
That has a whole ‘nother meaning in Honduras. My brother volunteered at an orphanage over the years. In passing he mentioned a mom and dad visiting their child for the first time in three years. “Huh??”
He said most of the kids had parents, but the parents were unwilling to take care of them, so dumped them on the streets like a dog. They would even have siblings that still (for now) lived with the parents!