Nearly eight million old-fashioned vinyl records have been sold this year, up 49% from the same period last year, industry data show. Younger people, especially indie-rock fans, are buying records in greater numbers, attracted to the perceived superior sound quality of vinyl and the ritual of putting needle to groove.

But while new LPs hit stores each week, the creaky machines that make them haven’t been manufactured for decades, and just one company supplies an estimated 90% of the raw vinyl that the industry needs. As such,...