Sometime around 1877-1878, it is believed that then United States president Rutherford Birchard Hayes was recorded giving a speech (Often cited to be his inaugural address) by inventor Thomas A. Edison and other collogues with the latter’s tinfoil phonograph. This recording, if it does exist, is the first known audio recording of a U.S president, and one of the earliest recordings of the human voice. The tin cylinder containing the recording is believed to have been lost between 1878 and 1900, being misplaced (unsubstantiated rumors of it being destroyed also exist). Due to the age of the recording, the lack of proper preservation, and little interest in finding it, this recording has almost no chance of being found. Although some have theorized that it still exists in the Rutherford B. Hayes Presidential Library & Museum archives or in one of many collections of Edison's early works, this has never been confirmed, and likely never will be.
In December 2020, a video claiming to contain this audio was uploaded to YouTube. This caused a brief surge in notoriety for the recording. The audio was later found to be an actor reading a script for this documentary: https://www.youtube.com/watch?v=jHEN2vLe5Rk&t=0s
Due to it’s elusive nature, impracticality of recording audio at the time, and lack of evidence, many believe that the recording never existed, though this has never been proven true or false.
Sources[]
1:https://www.cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/r/Rutherford_B._Hayes.htm#:~:text=Hayes%20is%20also%20reputed%20to,recorded%20on%20has%20been%20lost. (Archived wikipedia page mentioning the recording)
2:https://www.cnn.com/2011/11/20/opinion/greene-candidates-appeal/index.html (CNN news article discussing this recording)
3:https://www.youtube.com/watch?v=X8piwAWJxCw (Hoax video claiming to be this speech)