Xerox in the 1940s? Xerox can trace its roots to 1906, but I don't think they were offering stocks until later. In 1958 the company Haloid its name to Haloid Xerox, reflecting its belief that the company's future lay with xerography, although photography products were still more profitable. That balance quickly changed with the success of the Xerox 914 copier. Introduced in 1960, it was the first automatic Xerox copier, and the first marketable plain-paper copier. The company could not afford a blanket advertising campaign, so it placed ads in magazines and on television programs where it hoped business owners would see them. The company also offered the machines for monthly lease to make xerography affordable for smaller businesses.
Demand for the 650-pound 914 model exceeded Haloid-Xerox's most optimistic projections, despite its large size. Fortune later called the copier "the most successful product ever marketed in America." Sales and rental of xerographic products doubled in 1961 and kept growing. In 1961 the company was listed on the New York Stock Exchange and changed its name to the Xerox
Back then, the big blue-chip companies were considered the best things to buy if you were in it for the long term.
How about AT&T which has been offering stocks in some form and under various names since the 1880s? Ford, GM, or other US car companies?
Coca-Cola might be a good choice, but I can't remember when it was first listed on the NYSE. I suspect it was before the 1940s.