Yes, Trump DID create the problem, like it or not. 

He cancelled programs specifically designed to keep people in their home countries. The "remain in Mexico" policy, combined with the lack of vetting by that administration, led to the flood of immigrants when he left office. Currently, Trump has fired 100's of immigration judges, leading to a system that can't do the normal work the system already had, leading to the current surge in deportation by ICE of people that haven't kept up on their paperwork, because the current office occupants broke the system. 

The problem is, currently, the "right" is working on a whole bunch of false assumptions, lies, and general ignorance. 

For instance, no one here has been able to tell me how to do immigration the "right" way. That should be the minimum for any kind of discussion.