This may be off topic for this subreddit, but I am trying to do a family tree for my family and I can't seem to find any information. I am trying to find information on my Great Great Grandfather. He was born in 1888 in Istanbul. Are there any Ottoman birth, military, or marriage records from this time I would be able to look through?
Also, he was Sephardic Jewish. Would synagogues in Istanbul have kept birth and marriage records of the people in the congregation?
Yes, the Ottomans carried out a number of censuses.
Unfortunately you would likely need a specialist to go through them as they will have been written in Ottoman Turkish. That is to say, in 1928 the Turks reformed their language from having been written in the Arabic script to being written in the Latin script. So any government documents from before 1928 will have been written in a script that even native Turkish speakers cannot read today.
I'm unfortunately not specialist enough to know about the question of Synagogues, but insofar as that narrows things down quite a bit I suspect that that might be a good avenue by which to approach the issue.