Dave,
If I understand your question the current Grand Central Terminal was completed in 1913. Grand Central Depot, which preceded the Terminal was completed in 1871. It was rennovated (enlarged) in 1898 but it did not expand the train capacity and the increase in traffic volume had created a need for more tracks. This need for more tracks, and the requirement to electrify the tracks coming into Grand Central as a result of the 1902 train crash in the Park Avenue tunnel, were major factors in the planing and construction of the current Grand Central Terminal. I believe construction began shortly after the city granted the New York Central certain subsurface rights in 1903.