Amalek was the first nation to harass the Israelites after the great and open miracles they experienced (see Exodus 17:8–16) ; other nations then followed their lead.

The Rabbis say: [When describing the attack of the Amalekites, the verse employs the term: “Encountered you [karekha]” (Deuteronomy 25:18). This teaches that the Amalekites cooled you [hikrekha] before anyone else. Rabbi Hunya said: To what is the matter comparable? It is comparable to a scalding bathtub into which no creature was able to descend. One ruffian came and leapt into it. Even though he was scalded, he cooled the water for others. Here too, when the Israelites departed from Egypt, the Holy One, blessed be He, split the sea before them, and the Egyptians drowned in it. Fear of the Israelites fell over the nations…. When Amalek came and confronted them, even though the Amalekites received their just deserts through them and lost the battle, their attack cooled the Israelites, [i.e., lessened the fear of them,] before the nations of the world. (Tanĥuma, Ki Tetze)