Well, the answer is that the original plan for Washington D.C. didn't actually include a Supreme Court building. This is because courts, especially in the 18th and 19th centuries, don't require a whole lot of physical infrastructure. In a pinch, they can meet almost anywhere. (And sometimes they do, even today - the Oregon state Supreme Court currently meets in this nondescript two-story office building, sharing a building with a farming newspaper.) Because court can be held in almost any place with enough physical space for lawyers and judges, the Supreme Court used the Old Supreme Court Chamber from 1810-60 (which was a hand-me-down used by the Senate from 1800-6), and then the Old Senate Chamber from 1860-1935 (which was also a hand-me-down from the Senate). This was not a particularly pleasant environment for the Justices, who kvetched a lot about it.
Thus, for the first century-plus of its existence, the Supreme Court occupied the space in the Capitol Building that Congress wasn't using. This was irritating to Chief Justice W.H. Taft (yes, former President Taft), who pushed and finally successfully lobbied Congress to make two big changes to improve the Court's standing. First, Congress eliminated much of the Court's workload by allowing them to pick and choose their cases much more broadly with the Judiciary Act of 1925, 43 Stat. 936, so the bulk of the appeals work would be handled by the Circuit Courts of Appeal. Second, Taft finally lobbied Congress to build an independent Supreme Court building, which finally opened in 1935, after Taft's death. That's not to say that the Supreme Court Building wasn't unopposed - the poor conditions in the Old Senate Chamber meant that the Justices had excuses to work from home, and many of them did. Justice Louis Brandeis flatly refused to give up WFH, and never moved into his designated office space, even after the Supreme Court building opened.
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