Expand LEGAL immigration.
Go ahead and build a wall. But put a door in that wall. Instead of putting false quotas, let a free market restrict the flow.
Bar anyone with a criminal record. (Establish an exhaustive appeal process for the reformed)
Everyone entering must undergo background checks. (The migrant could be responsible to pay for all or some of the cost of this process. There could be a special tax rate that would apply to those in a temporary probationary state to recoup cost of screening, instead of funding the social programs they are barred from benefiting in)
Everyone allowed to enter would be on a sort of probation (state run) for a time. They must provide for their own needs (no gov assistance) and moving around must be requested/permitted by their case worker.
Any break in this or failure to report results in deportation proceedings.
After a set time (24-48 Mo? Partly set by the time it would take to pay cost of screening to the fed gov {while state taxes pay the cost to monitor them})they can get a normal green card and begin the process of becoming a citizen.
This puts the individual in a position to prove themselves the type of person that builds this great nation. It puts the free market back in control of the economy and work force (instead of gov reg). It would create fully funded jobs across the states and put individual states in control (instead of big gov) of the migrants here and the numbers their states can handle.
Perhaps most importantly, it creates opportunity for the many industrious individuals in pursuit of life liberty and happiness, who cannot show on paper the strength of their character to come help build a great America.
Finally this would free up enormous amounts of border resources that are wasted catching people who are no danger to the us and only want to participate in our economy. The only people trying to cross the border illegally would be those with ill intent and our Patrols could focus on those individuals only