If, by Black Plague, you mean outbreaks of infection by the bacterium Yersinia pestis, then the answer is "absolutely!"

Prior to the Black Plague of the 14th century, the so-called "Justinian's Plague" has definitively been linked to Yersinia pestis infection (this paper has details: https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(13)70323-2/abstract). The evidence comes from DNA located in human remains known to have died from plague which has been identified as coming from one strain of Yersinia pestis. Justinian's Plague is thought to have killed between 25 and 50 million people or 10-15% of the world's population at the time.

Additionally, there was a more modern pandemic in the late 19th to very early 20th century that originated in China. Modern DNA sequencing similar to the paper I linked above has suggested that populations of small mammals like marmots & rodents in China are a good contender for the Yersinia pestis reservoir.

More inteestingly, more DNA evidence has come to light that plague is a fairly ancient disease in human terms and was infecting humans around 5,000 years ago.

Of course, there may be more outbreaks of Yersinia pestis infection that we don't know about. They would go "below the radar" because such outbreaks may have ravaged a village or two before burning themselves out. A case in point is the Thirty Years War that saw the Germanies lose 25-33% of their populations through "war, famine & plague". To the best of my knowledge, "plague" in that context does not necessarily mean Yersinia pestis infections but it could have and we might not have any evidence left to know for certain.

So, if you're asking if people died of "plague" before the Black Plague then the answer is also "absolutely!". The problem is that plague is a catch-all term that could mean many different infectious diseases with similar symptoms. This is because, while the modern definition of plague refers to an infection of Yersinia pestis, such infections can be bubonic, septicemic or pneumoniac in nature. Absent modern diagnostic tools, it is difficult to trace all of them back to the same bacterium. In particular, pneumoniac plague is similar to other diseases of the respiratory tract just with a more rapid onset and mortality.