Rumours about this have been circulating since 1998 and the National Park service commissioned a study to investigate the matter. The historians in charge have found no evidence for this. Quoting from the executive summary:

The statue's design almost certainly evolved from an earlier concept Bartholdi [the Statue's sculptor] proposed for a colossal monument in Egypt, for which the artist used his drawings of Egyptian women as models. Bartholdi’s preliminary design for the Statue of Liberty is consistent with contemporary depictions of Liberty, but differs markedly from sculptures representing freed American slaves and Civil War soldiers. Bartholdi changed a broken shackle and chain in the statue's left hand to tablets inscribed "July IV, MDCCLXXVI” (July 4, 1776) at Laboulaye's request, to emphasize a broader vision of liberty for all mankind. There is no evidence that Bartholdi's “original” design was perceived by white American supporters or the United States government as representing a black woman, or was changed on those grounds. (...) We found no corroborating evidence that Edouard Laboulaye [who originated the idea of the Statue] or Auguste Bartholdi intended to depict Liberty as a black woman. Laboulaye’s intent was to present a monument that would commemorate the fulfillment of America’s commitment to universal liberty established by the Declaration of Independence, and set an example for other nations.

The "colossal monument" referred above was a gigantic lighthouse Bartholdi proposed to the Khedive of Egypt, Ismail Pasha, for the entrance of the new Suez Canal. It would have been named "L'Egypte éclairant l’Orient" (“Egypt Bringing Light to the Orient”) and was eventually rejected by the Khedive. The main character was a “fellah”, a rural Egyptian woman in traditional dress. While some Egyptians can be considered as black, orientalist representations of fellah women in the nineteenth century gave them a North African/Middle Eastern appearance. Examples:

• Émile Vernet-Lecomte, 1864 Femme fellah portant son enfant
• Charles Landelle, 1866 Femme fellah
• Elisabeth Jerichau-Baumann, 1872 Egyptian fellah woman

What is true, however, is that the Statue of Liberty, while always dedicated to liberty in the broadest sense, was at first linked with the end of slavery. Quoting again the executive summary:

The Statue of Liberty would never have been conceived or built if its principal French and American advocates had not been active abolitionists who understood slavery as the cause of the Civil War and its end as the realization of the promise of liberty for all as codified in the Declaration of Independence. But the Statue of Liberty was not intended entirely as a monument to the end of slavery.

It only started to be associated with immigrants in the early nineteenth century.

The "immigrant" interpretation gained momentum in the 1930s as Americans prepared for war with Hitler and by the 1950s, it had become the predominant understanding of the statue's original purpose and meaning.

So, no, the Statue of Liberty was never a Black woman, and it drew inspiration from a previous project that had a North African woman as subject. Its conception was linked to American/French abolitionist perspectives, but it was from the start about liberty "for all mankind".

Main source

Joseph, Rebecca M., Brooke Rosenblatt, and Carolyn Kinebrew. “The Black Statue of Liberty Rumor: An Inquiry into the History and Meaning of Bartholdi’s Liberté Éclairant Le Monde, Final Report.” Northeast Region Ethnography Program, National Park Service, September 2000. https://digitalcollections.usfca.edu/digital/collection/p15129coll15/id/9/.