You can directly appeal to SCOTUS from highest court in each state. And then you can collateral appeal the conviction through habeas corpus. In practice, SCOTUS

You can directly appeal to SCOTUS from highest court in each state. And then you can collateral appeal the conviction through habeas corpus. In practice, SCOTUS almost always denies cert on direct appeals in state criminal cases, even though it ends up hearing a small handful of them on collateral appeal-the fact you almost never succeed in getting a hearing is why some people seem to wrongly believe you can’t ever. But this is far from a normal case.