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Elephants had gone extinct in Egypt by about 2600 B.C. or so, plus or minus a few centuries. So for a very long time there was no native elephants for Egyptians to use. It is theoretically possible that the Pharaohs might have imported some for military purposes, but I'm not really seeing any sign of this.
Regardless, by the time Ptolemy I established himself in Egypt, he had to start his own elephant force from scratch. He was motivated by his experiences under Alexander the Great, which taught him how potentially powerful elephants could be. And also because his rival Seleucus was building an army of war elephants.
The early Pharaohs' obsession with ivory, along with changing climatic conditions, had driven indigenous elephants completely otu of Egyptian territories. When Ptolemy I learned that the lands south of Egypt contained elephants, he began to preparations to collect and train his own indigenous elephant force ... [Ptolemy's son Philadelphus] took up the collection of war elephants.
- Kistler, John M. War Elephants. University of Nebraska Press, 2007.
Alternatively, it is also possible that the Kushites used war elephants before this while they ruled Egypt. Though, I'm not sure if you want to consider this "use ... by Egyptians" per se.
The Kushites (Ethiopians) used war elephants long before Macedon, according to Arrian ... the Sufra Great Enclosure may have been a center for training war elephants, as there are ramps allowing them to move easily between buildings. Unfortunately, our understanding of the Kushites is sparse and few records exist. As to the time when Kush used war elephants, the evidence cannot prove a pre-Ptolemic tradition of the practice.
- Kistler, John M. War Elephants. University of Nebraska Press, 2007.