U.S. Constitution, Article III, Section 2,
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, [...]
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.
Because the demand by Chairperson Cummings, is based on the Laws of the United States, the Supreme Court only has appellate Jurisdiction.
To change that would require a Constitutional Amendment.
In Marbury v. Madison, 5 U.S. 137 (1803),
Congress does not have the power to pass laws that override the Constitution, such as by expanding the scope of the Supreme Court’s original jurisdiction.
For those who have read the details of the complaint; in THE CONSTITUTION OF THE UNITED STATES OF AMERICA ANALYSIS AND INTERPRETATION, concerning the Investigatory Power of Congress, pages 95-96:
One limitation on the power of inquiry which has been much discussed in the cases concerns the contention that congressional investigations often have no legislative purpose but rather are aimed at achieving results through "exposure" of disapproved persons and activities: "We have no doubt," wrote Chief Justice Warren, "that there is no congressional power to expose for the sake of exposure." Although some Justices, always in dissent, have attempted to assert limitations in practice based upon this concept, the majority of Justices has adhered to the traditional precept that courts will not inquire into legislators' motives but will look only to the question of power. "So long as Congress acts in pursuance of its constitutional power, the Judiciary lacks authority to intervene on the basis of the motives which spurred the exercise of that power."
As requested in a comment, I have added some references to cases (or controversies) involving original jurisdiction.
The judicial power extends to controversies between two or more states and the Supreme Court was given original jurisdiction in which a State shall be Party. Some of those cases are:
Rhode Island v. Massachusetts, 37 U.S. 657 (1838), the court was asked to ascertain and establish the northern boundary between the states [...].
Nebraska v. Iowa, 143 U.S. 359 (1892), the Court was asked to fix the boundary due to changes in the path of the Missouri River.
New Jersey v. New York, 283 U.S. 336 (1931), The State of New Jersey sued the State of New York and the City of New York to enjoin them from diverting water from nonnavigable tributaries of the Delaware for the purpose of increasing the water supply of the City. Pennsylvania intervened to protect its interest in the river.
And, New Jersey v. New York, 523 U.S. 767 (1998) ownership of Ellis Island, as mentioned in the comments.