It heavily depends on what, exactly, you mean. If, for example, you are talking about the 19th or 20th century, when records were fairly good across the board due to modern bureaucracy, modern administration, and modern record keeping then yes. It's not an especially difficult task. If however, you are asking with regards to a specific era besides that or some specific metric beyond the immediately obvious ones then the question is a lot murkier, especially since the farther back in time we go back the harder and harder it is to find good, dependable, and full documentation to work with. Even for fair chunks of the early modern period, you have to work with reasonable estimates that you can cobble together from available data.

It also depends on what you mean by wealth. If by wealth you mean the net value of all the production and all the assets in the nation then that is easily answerable: it's the modern day United States. In general, the modern day world is full of some of the most wealthy and prosperous economies in human history, simply because we are both so much more efficient at production and so much more populous than we were even a mere 100 or 50 years ago. A mid-sized, average nation today can outproduce and is, by most practical metrics, wealthier than even some of the largest and richest empires in history (excluding the more modern ones, of course). So, of course, the large, economic giants of today are the wealthiest, most productive states in human history.

If, however, you want to talk about relative wealth, the question becomes murkier and you again have to depend on what essentially amount to educated guesses/estimates. And this is by no means criticizing or casting doubt on these estimates and their worth, however, they are a casualty of an era where we simply we weren't as good at record keeping.