If ICE arrested you, would it be fair for them to deport you before you were able to present evidence that you're a citizen?

Due process doesn't mean a full trial. At its most fundamental level, it simply means having a fair process. Of course there's a whole set of case law behind determining what is fair, and a lot of that depends on the type and severity of the case.

But what happens if all that fairness and case law is ignored? Without due process (such as a hearing with a judge), how do you prove you're a citizen? Who do you even present your evidence to? How can you even gather your evidence if you're locked away in a cell?

When people argue for due process (which is a constitutional right), this is what they're arguing for. They're arguing that a single government employee should not be able to deport them without a fair process. Which is a constitutional right for all people (not just citizens), per the 14th amendment.