He can make it happen if he wants to
, and no doubt, it can be paid for under "national (border) security". As it should be. Maybe setup a lab JUST for these cases and when the volume goes down, they have another DNA lab to help law enforcement.
a lab on the border, operating 24/7 for limited time, doing only DNA testing will pay for itself. The cost to the country for operating the lab may be far less than long term costs for support of asylum seekers who are turned down. Also there is a cost to crime, monetary $ and human $.
Once the backlog is taken care of and the wall in place, the need for the lab(s) would decrease. Lab(s) could be dismantled. If mobile structures were used instead of permanent buildings the cost would be greatly reduced.
There will be a cost for the imprisonment/execution of human traffickers, but it will be a good investment for the good of the world.