The first European/white Jew to visit Beta Israel was Joseph Halévy, a French scholar of Semitic languages who also spoke Amharic (by then the regional Ethiopian language) and Ge’ez (the local liturgical language among Beta Israel). In addition to teaching, he also worked for the Alliance Israelite Universelle, a French Jewish organization that saw it as its mission to provide education, culture, and material improvements to various MENA Jewish communities, many of which suffered from endemic poverty and persecution.
They did a lot of good in many ways throughout the Jewish MENA (they did great work in having antisemitic laws and accusations struck down, for example), most notably through their French-language Jewish schools, though much of this involved secularizing and Westernizing long-standing Jewish communities to mixed response.
It should be noted that while we said that Halévy was the first white Jew to visit Beta Israel, that’s not quite true, and that becomes important here. The first, in the early 19th century, were actually technically Christians- Jewish converts to Christianity who became missionaries and who, alongside born-Christian missionaries, were sent to Ethiopia to minister to existing Christian communities and convert non-Christian ones.
When they discovered the existence of tribes there who considered themselves to be Jewish**, they were fascinated and attempted to launch a missionizing project. There was a tremendous backlash from the group, especially the priest Abba Mahari, and in the end, only a small proportion of Beta Israel ended up converting to Christianity.
It was the reports of these missionaries that first made the Alliance Israelite Universelle aware of this tribe that apparently considered itself Jewish, and that prompted the group to send Halévy to investigate in the late 1860s, as he would be able to communicate with them in their language.
He at first reported them as being very suspicious of him and he had initially hidden his Jewish faith from them, but when he asked them if they were Israelites (they didn’t recognize the word “Jew”), they affirmed this to be true. When he told them that he too was a “Falasha” (the local derogatory term for Beta Israel), they were confused and doubtful- how could there be a white Falasha?
It really doesn’t seem to me from Halévy’s description of the conversation that they were convinced they were the last Jews, per se- in their conversation, they asked Halévy if he had ever been to the Temple in Jerusalem, which they wouldn’t have asked if they thought they were the only Jews- but it does seem clear that if they believed there were other Jews, they were not expecting them to be white.
Beta Israel and Halévy got along on his visit, but his connection with them ceased after his trip. He returned to the Alliance Israelite Universelle headquarters in France, brimming with reports of these Jews, but was unable to convince the organization that these were Jews and therefore worth helping and funding.
It wasn’t until 40 years later that Halévy’s student, Jacques Faitlovich, returned to Ethiopia, and by that point, Beta Israel ware gunshy when he claimed that he was a Jew- the community had deteriorated into increased poverty at that point (it had already been a poor, oppressed, and nearly isolated community within Ethiopia for centuries) and were tired of encountering missionaries who claimed to be Jews in order to convince them to convert.
Faitlovich did end up warming them up to him, though, and became the community’s biggest advocate worldwide for the rest of his life, raising money, working to educate young men from the community at Jewish schools in Europe and Palestine, and establishing a Jewish school in Addis Ababa staffed in part by some of the boys who he had helped educate.
Note: Especially once the Alliance and Faitlovitch have been mentioned, it’s worth mentioning that Faitlovitch was seen as a controversial figure and fought an uphill battle on behalf of Beta Israel. The first student he sent to a European Jewish school, a boy named Daniel who he attempted to register in an Alliance school in Paris, was rejected as non-Jewish- they believed he’d been bought in a slave market. The later boys he sent were more commonly accepted, generally at Orthodox Jewish schools in Germany, England, Italy, and Palestine, but faced a great deal of hardship including social isolation and illness (many of them died young).