Yes, some of them had. I have an old camera that do have a selv timer.

Self timers, rubber bulb releases, Speed Graphics with
solenoid shutter releases and clever kluges with strings and
levers have been around a long time.  My Mom's old folding
Kodak has a cable release socket (first serious camera I
used--it had f/stops and shutter speeds) and it predates
your photo.

Consider also that it could have been a relative or neighbor
that made the shot, my wife's family had a similar riddle
until we asked an older family member.

darkroommike