Immediately block any Mexican auto or other product from crossing the border.
They’ll get their attention, pronto !
Better still, tax all remittances send to Mexico at a rate of 50% until Mexico shows a genuine effort to curtail mass illegal immigration. Promise to reduce that to 20-25% if and when legitimate measures are taken. About 8% of Mexico's GDP is remittances sent from Mexican nationals and their families in the US - that rate is much higher for many Central American countries.
As these people move north we will be able to tell where they have intend to cross. Surge a pile of BP agents into that sector and shut the ports of entry. Force the Mexicans to turn them around.