The Internet Archive has a recording of Arthur C. Lichty singing MY LITTLE GIRL on an Edison cylinder from circa 1915.

You can also hear an instrumental version by Conway's Band from a 78-rpm record, Victor 35495-A, circa 1915. It's the first tune in a 4-tune medley: (1) MY LITTLE GIRL, (2) PUT ME TO SLEEP WITH AN OLD-FASHIONED MELODY, (3) AT THAT SAN-FRAN-PAN AMERICAN, and (4) HOP A JITNEY WITH ME.

These are free downloads in various formats.