Accounting and bookkeeping are some of the oldest professions, with evidence for their existence dating back over 7,000 years, to the neolithic (stone age) period. In fact, the advent of accounting is largely responsible for the advent of written numbers and language. Back then the largest business organizations were effectively governments, but the fundamentals worked out the same way: whether it's an empire or a corporation all that really matters is that the wealth keeps flowing. And to achieve that you don't need the massive data crunching and networking abilities of modern computers, a modular structure works just fine.

Every transaction involves a human, so there's the capability to keep track of the transactions if you have the staff to do so. From there it's mostly a matter of summary data being transmitted elsewhere, and then summaries of summaries. A 4th century BCE empire would still have access to a great deal of data regarding the business of the empire but primarily it only needs the summary data. How much grain was grown in an entire province, for example, rather than who grew it and where and so forth. Data that may exist in records some where or merely in some clerk's head, but for the most part data that isn't hugely relevant and not worthy of the cost of trying to keep track of it at every level.

Much of the historical record in the form of written language from the most ancient civilizations is actually just accounting data. Interestingly, a lot of the historical, versus archaeological, evidence we have about the bronze age collapse is in the form of requests for grain between different parts of empires and other forms of administrative correspondence.

Until the present day it was necessary for any organization needing to perform accounting for its activities needed to employ a great number of people to do so, depending on scale. The Romans, for example, employed an enormous number of scribes, clerks, and tax collectors. And the British as well as Dutch East India Companies employed thousands of clerks. Throughout history millions upon millions of people have served as record keepers, accountants, clerks, etc. For a very long time the term "computer" referred not to a machine but to an individual who performed computations by hand, and there were a great many of them employed prior to the advent of electronic computers.

As a recent example, consider IBM. They did not spring to life in the computer era, they began decades prior, as the "Tabulating Machine Company" dating back to the 1880s. Their earliest lucrative business was in providing automated tabulating machinery using punched cards to the US Census bureau to aid in the censuses of 1890 and 1900. By the 1940s the company had grown to have revenues above $100 million (nearly $2 billion adjusted for inflation for their 1945 revenue), so you can imagine how widespread use of their equipment was. So you can imagine the total revenue of all the companies that used their equipment. And if you think about the fact that for the most part such equipment was used to replace clerks, that gives you some idea of the scale of the total number of clerks employed at the time.