The Supreme Court has extremely limited original jurisdiction. This is the paragraph that outlines the Supreme Court's original jurisdiction: In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.
Having said that, it is thoroughly possible to set up a case that would fall under the original jurisdiction of the Supreme Court so that it can start out in a lower court - and it's highly recommended that you do. This is because if you start out suing someone in the Supreme Court and you don't get the answer you want, there's nowhere to appeal to. Let's say the State of Idaho decided to sue the State of Washington because Washington wasn't doing enough to stop Idahoans from buying weed in their dispensaries and bringing it home with them. If the case is captioned State of Idaho v State of Washington, it's gotta go to the Supremes...and the Supremes are very likely to point out it's not Washington's job to keep Idahoans from buying pot. But if it's captioned Brad Little vs Bob Ferguson, it can be tried in a district court; when Idaho loses they can appeal to the Supremes and lose again.
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