Here is something they have already done -- The caravanors have filed a class action lawsuit in the DC District Court. The nominal defendants are Trump ("our President") and others
They seek preemptive declaratory relief that Trump has violated their (procedural and substantive due process) rights rights under the 5th Amendment.
"Trump’s professed and enacted policy towards thousands of caravanners seeking asylum in the United States is shockingly unconstitutional."
Trump seeks to prevent them from "exercising their lawful right to seek asylum in the United States"
So, non-citizens who have not "set foot on" US soil are suing for "professed" actions, including for "adequate temperature control and ventilation" in the tents theyve never seen (see my post 2 up^).
https://assets.documentcloud.org/documents/5026840/11-1-18-Pineda-v-Trump-Complaint.pdf