The earliest work of fiction I can find that depicts an animated Egyptian mummy is the 1827 novel The Mummy! by Jane C. Louden.

The eventual imperial control of Egypt by the British in 1882 gave the English-speaking world even greater access to the tombs of Ancient Egypt, and the golden age of Egyptology really flourished.

This increased exposure and the wonder it caused in people continued to capture the imagination. In 1892, the ever popular Arthur Conan Doyle wrote a short story called Lot No. 249 which featured an Oxford student reanimating an Egyptian mummy and sending it on a killing-spree.

My amateur opinion (this is waaay outside my specialty area) is that early Egyptomania and Frankenstein by Mary Shelly inspired Loudon's novel. Increased exposure to Egyptology and Loudon's work inspired Doyle, and Doyle inspired the Hollywood monster and everything that followed.