ok dont quote me but ive looked into various companies histories just for the heck of it
the best source is on the manufaturers websites themselves as most today were formerly a company that does not exist anymore thru the mergers/aquisitions mentioned before

the first real material handling company is one that still exists today
Clark
in 1917 they built a machine called the tructractor to haul parts around their axle manufaturing facility
some customers had seen the machines and had clark build some for them
in 1918 they sold 8 of them lol
they had no forks though
the first real forklift was an electric yale in 1925
it did not have hydraulics it used a gear and ratchet system to raise the forks
hyster came out not long after
also baker (now linde) who made eletric vehicles since the turn of the century came out with a coil ram truck in 1920 (jay lenno has a 1908 baker electric car and i saw an identical one last year at lindes plant in sc pretty cool) they made the 1st sit down controls for operators in 1930
they were also formerly otis and linde/baker
then you have towmotor of course (i cant find an actual start up date for them) that was bought out by cat in 1965 and is now part of MCF (joint venture 1991)

again google is your friend on these matters lol
post more history if you find it it is pretty interesting
(those old machines look less safe than sticking your arm in a wood chipper lol)