At the time and place that your dad was born, Christian babies didn't usually get government birth certificates but their christenings would be recorded at churches. Since your dad was Jewish in Russia, his birth might have been on record at the local synagogue. However, with the pogroms and the revolution, they might have been lost. It might require someone doing the actual footwork over there to track it down.
Another source would be immigration records. That might be your best bet.
US Census records are another possibility.
There was no local synagogue in my dad's village in 1892. My dad tried to get some info about this village and nothing was left . There was one piece of paper for the whole family when they came here and it had some info on it. When dad dies one of his brother wanted the document and my mother refused to give it to him. I think my
ex brother now has is . I went the army office at my city hall and they only had on record the date my dad picked out for his DOB. I was told I would have to go to Boston to get some more info. If you can get the long form birth certificate you can work your way backward to find out who are your ancestors .
That is how I found out I had an uncle , I used the US Census records . I was doing this more for my mom , most of her family was buried at the family cemetery .
Her parents and some of her brother ,one of her favorite sisters that was only in her 20's dies and was buried at another cemetery . My mom was really upset about this
b/c she wanted to buried with her beloved sister and to made matter worst her sister headstone was no long standing. My mom was a little a little girl and couldn't
remember her sister DOB or DOD so I had to make a lot of phone calls and a lot research . I was able to find the DOD so as my last resort I called the city hall of where my aunt was born and told them that I was trying to find my aunt DOB so we could put a stone down in the cemetery so my mom could be buried in peace knowing her sister name was there too. The woman was very moved by this and found my aunt DOB , we had a stone made with her name and DOB and DOD and place it on the ground in front of her parents headstone. I was named after my aunt so this was very close to me too. My mom was able to dies knowing her beloved sister name was
close by. I got so interested in doing my mom research I decided to do dad too. It's was very interesting doing my mom family I was able to find the ship manifesto
for her family ,her mom was born in Russia too and her dad in England . They met in England and came USA together .