St. Athanasius of Alexandria (ca. 296-373) in his Oratio de incarnatione Verbi (On the Incarnation of the Word) suggests reasons why Jesus Christ chose to rise on the third day after his death, rather than sooner or later.
Why did Christ not rise immediately after He died? “He could, even immediately on death, have raised His body and shown it alive; but this also the Saviour, in wise foresight, did not do. For one might have said that He had not died at all, or that death had not come into perfect contact with Him, if He had manifested the Resurrection at once.” That is, some might have thought He did not die, but merely passed out.
Why did Christ not rise after one or two days? “Perhaps, again, had the interval of His dying and rising again been one of two days only, the glory of His incorruption would have been obscure. So in order that the body might be proved to be dead, the Word tarried yet one intermediate day, and on the third showed it incorruptible to all.” People knew from experience that the natural process of decay is well underway and visibly discernible by the third day after death.
Why the third day, and not later? Athanasius gives three reasons:
One reason is so that no one would think that the body, long since decayed, had been removed, and a living person put in its place: “But lest, by raising it up when it had remained a long time and been completely corrupted, He should be disbelieved, as though He had exchanged it for some other body.”
A second reason is so that the memory of His dying would be fresh in their minds, for one might distrust a distant memory: “A man might also from lapse of time distrust what he saw, and forget what had taken place—for this cause He waited not more than three days.”
A third reason is so that those who expected Him to rise would not be kept in suspense for too long: “Nor did He keep long in suspense those whom He had told about the Resurrection: but while the word was still echoing in their ears and their eyes were still expectant and their mind in suspense, and while those who had slain Him were still living on earth, and were on the spot and could witness to the death of the Lord’s body, the Son of God Himself, after an interval of three days, showed His body, once dead, immortal and incorruptible.” (26)
Quotations from A Select Library of the Nicene and Post-Nicene Fathers of the Christian Church, Second Series, Vol. IV, ed. Philip Schaff and Henry Wace (Edinburgh: T&T Clark, 1886).