In New York, the District Attorney is obligated to provide the accused any information which is exculpatory or potentially exculpatory, without any request by the defense. Additional materials are discoverable once requested by the accused. Further discovery is available if initiated by the defendant.
The time-line of discovery in a particular case ranges and depends on a variety of factors, including, the complexity of the case, the number of cases currently pending in the court hearing your case, and the efficiency of the attorneys.
To initiate discovery, counsel must submit the demand for discovery within 30 days after arraignment on the indictment in a felony case or the first appearance of counsel, whichever is later. Once triggered, there are time-limits for the discovery process. However, the clock does not simply stark and continue running. At various points, the clock may start and stop. For instance, if your attorney requests an adjournment, the clock will likely stop until the next court appearance.
Another factor in the time discovery could take is based on tactics. Sometimes, it is better to move quickly, while in other cases it may be better to move a little slower. It depends on the unique facts in your case.
In other words, this question simply does not have a clear-cut answer.