At this point in the novel, James Ramsey is six years old and irrational in his estimation of the value of things.  The thing James anticipates, which the reader may guess is the trip to the lighthouse, never takes place when he is six.  That turns out to be the least of his losses.  In retrospect, from the end of the novel, the great event in the first three sentences is Mrs. Ramsay's ability to construct a world of relatively stable expectations and fulfillments for her children, shielding them from the terrible capriciousness of the world which will destroy many of them before the novel's end, when they have moved outside her protective realm. 

Mrs. Ramsay will die in the "Time Passes" section III in a bracket insertion describing her husband, walking half-asleep in the corridor, putting his arms out for her, "but Mrs. Ramsay having died rather suddenly the night before, his arms, though stretched out, remained empty" (194).  Her daughter, Prudence, whom we haven't even met in the first three sentences, is married after her mother's death in 'Time Passes" (198), and Prue is dead in childbirth a page later (199).  Two pages later, James' elder brother, Andrew, is among "twenty or thirty young men" killed instantaneously by a single artillery shell in World War I.  In "The Lighthouse," the novel's third section set ten years after the first, James finally will sail to the lighthouse with his father and his surviving sister, Cam.  The visit will become a test of wills between James and his father, the boy seeking praise from the old man and the old man grudgingly giving it, while Cam looks on. 

Outside anything we could predict from the first three sentences is Lily Briscoe's vision, the artist who observes the whole family on the first day, and who returns to the house on the day ten years later to paint.  She is the only one in the plot who realizes Mrs. Ramsay's centrality in the family dynamic, and she translates it into her painting with tragic certainty as "a line there, in the centre" that is both Mrs. Ramsay and the Lighthouse.