Some days ago the Moscow state arhcive (CGA of Moscow)  posted on its website the metric books of Moscow Synagogue from 1870 to 1918 (births, marriages, deaths and divorces). That are colour scan files.
Moscow vital record were оnly in Russian (no in Hebrew)

Link to metric books
https://cgamos.ru/inye-konfessii/iudaizm/2372-1-1/ (1 means the number, for example from 1 to 46, 1 is birth records of 1870)

If you know the date and year it is simple to find the record.

The year | Numbers of births folder
1870    1 https://cgamos.ru/inye-konfessii/iudaizm/2372-1-1
1871    1 https://cgamos.ru/inye-konfessii/iudaizm/2372-1-2
1872    1 https://cgamos.ru/inye-konfessii/iudaizm/2372-1-1
1873    1, 2 https://cgamos.ru/inye-konfessii/iudaizm/2372-1-1 or https://cgamos.ru/inye-konfessii/iudaizm/2372-1-2 and so on
1874    1
1875    1, 5
1876    1
1877    7, 31
1878    31
1879    31
1880    31
1881    31
1882    32, 34
1883    34
1884    32, 34
1885    32
1886    32
1887    15, 35
1888    17, 35
1889    35
1890    19, 37
1891    37
1892    37
1893    37
1894    37
1895    37
1896    37
1897    22, 33
1898    33
1899    33
1900    33
1901    33
1902    33
1903    33
1904    33
1905    40
1906    40
1907    40
1908    40, 34
1909    40, 34
1910    43
1911    43
1912    43
1913    43
1914    43
1915    43
1916    44 https://cgamos.ru/inye-konfessii/iudaizm/2372-1-44
1917    44 https://cgamos.ru/inye-konfessii/iudaizm/2372-1-44
1918    44 https://cgamos.ru/inye-konfessii/iudaizm/2372-1-44

I will place the index of surnames in English and Russian soon. Or you can write me to mail.

Sincerely, Yelena Volk
Yelena.v.volk@...