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The history of the Jews in Moscow goes back from the 17th century, although Moscow did not become an important Jewish center until the late 19th century when more Jews were legally allowed to settle. Prior to the 19th century, Jews had arrived in the city as prisoners of the Russo-Polish war or after 1790, as merchants allowed one month stays. In the late 1800s, the Jewish population boomed, and then dramatically dropped after the 1891 expulsion of Jews from the city. The population grew once again following World War I, and was a Jewish and Zionist cultural center until the end of the revolution, after which it became a Soviet Jewish center for a period of time. The Moscow Jewish community experienced a number of highs and lows under the Soviet Union as Jewish identity became increasingly taboo in the eyes of the government. After the collapse of the Soviet government and the mass migration of a huge portion of Russian Jews from the country, Moscow has still maintained a sizable Jewish population.
More here - https://en.wikipedia.org/wiki/History_of_the_Jews_in_Moscow
Moscow genealogical records are significant but almost wholly undigitised. It appears that one still needs to hire researchers to find historical vital records in 2019. Please request to join the group if you have Jewish ancestors from Moscow.