Shem MiShmuel

"On the third day Avraham lifted up his eyes and saw the place from afar." Rashi comments: Why did He delay showing it to him right away? So that they would not say that he was stunned and suddenly thrown into confusion, and that his mind was disturbed, etc.

But regarding the number of three days, one must consider why specifically three days, and not two or four. It appears that it is written, "In the third month after the children of Israel went out of the land of Egypt," the giving of the Torah took place. And in the midrash (rabbinic teaching) it says this is like the female convert, who must wait three months of examination.

And Maharal explains that the exodus from Egypt was a departure from the material. Until three months had passed, something of their former essence remained with them, but with the interval of three months they became completely distinct. For the first month is joined to the past, the third to the future, and the middle one is what divides and separates between them. This itself is the reason for the convert's three months of examination: so that she be completely separated from her former essence.

End of his words.

Now, regarding the test of the Akedah (the Binding of Yitzchak), it is stated in the books that the main test was that Avraham was a man of chesed (lovingkindness), to the point that he acted with kindness toward everyone who came into the world, even non-Jews.

And now he was commanded to perform a cruel act without equal: to slaughter with his own hands the son he loved more than his own life. This was the complete opposite of his attribute and his nature, from one extreme to the other. Through this his essence was tested, namely that he sets everything aside before the will of Hashem Yitbarach (G-d, may He be blessed), and is moved away from his attribute and nature to do the opposite, since such is the will of Hashem Yitbarach. To clothe himself in cruelty and to be cruel, he puts on cruelty.

Therefore one may say that this is the reason He delayed showing it to him for three days: so that he would be moved away entirely from his former nature and attribute, and there would be a complete separation between his former essence and his later essence. The first day is joined to the past, the third to the future, and the middle one entirely divides and separates, just like the three months there.