Trash haulers, beverage haulers, Newspapers
Many of these have dock to truck programs.
Both have training programs.
FedEx, XPO, Estes, Saia, take your pick of LTL haulers and many of them also have dock to truck programs as well.
Many little LTL final mile companies do too, or will take you on as a helper and work you into the license as they have a need or ability to.
But the best way for us to help is to know what area of the country you are in. Say Northeast, Southern California. Not too specific, but the nearest major city can help too.