The modern notion of "Gross Domestic Product" is usually attributed to Simon Kuznets, for a report to Congress "National Income, 1929-1932", which was delivered in 1934 (doesn't really come into its final form until the 1940s), although you can find elements of the idea much farther back in history.

Historically, there were various metrics of wealth and income for nations. If you were reading a 19th century newspaper discussing relative wealth of nations, they'd typically look at gold reserve as a measure of relative stature. Note that that _isn't_ a measure of income, its a measure of wealth.

One can find references all the way back to the ancient Near East to places that were wealthy and others that were poor. Because the Mesopotamians did their accounting on remarkably durable clay tablets, we have surviving an abundance of their accounting, they spent a lot of time calculating and collecting taxes. If you ask a man of the period "how rich is town X", the metric he'd most likely have had would have been the annual taxes paid.

Herodotus, cataloging the wealth of Babylon under Persian rule, does it with a mixture of measures of wealth, and measures of income

Among many proofs which I shall bring forward of the power and resources of the Babylonians, the following is of special account. The whole country under the dominion of the Persians, besides paying a fixed tribute, is parceled out into divisions, which have to supply food to the Great King and his army during different portions of the year. Now out of the twelve months which go to a year, the district of Babylon furnishes food during four, the other of Asia during eight; by the which it appears that Assyria, in respect of resources, is one-third of the whole of Asia. Of all the Persian governments, or satrapies as they are called by the natives, this is by far the best. When Tritantaechmes, son of Artabazus, held it of the king, it brought him in an artaba of silver every day. . . .

He also had, belonging to his own private stud, besides war horses, eight hundred stallions and sixteen thousand mares, twenty to each stallion. Besides which he kept so great a number of Indian hounds, that four large villages of the plain were exempted from all other charges on condition of finding them in food.

You can observe that there is little distinction between wealth and income, and that wouldn't emerge as a clearcut conceptual line until modern times. National accounts do recognize agricultural production as distinct from wealth -- eg you may _usually_ produce 100 bushels of wheat, but this year you produced only 80, and so have to go to buy food from someone else, these kinds of transactions occur very early.

In the 17th and 18th centuries, you find governments surveying economic activity in their country, doing kinds of almanacs of production, and producing tables for use in government offices. France was particular systematic about this, and Jean-Baptiste Colbert creates a model of systematic economic intelligence. He doesn't have any one metric; he wants to know about _everything_ in France and neighboring countries-- number of noble families, number of homes, number of soldiers. He's got no one measure of national income, but is gathering up a lot of data that enable him to make a stab at it, particularly in trying to get taxes paid.

Keeping the State solvent was the most clearcut empirical test of a national income. Kings borrowed and spent, and some years they were strapped and some years they were flush. Everyone in Europe understood the impact of the flow of American gold and silver on the solvency of the Spanish crown, for example; Phillip II could pay his armies with silver from Peru . . . that was a measure everyone understood.

A good example of what _wasn't_ well understood was the relationship between indebtedness, income, assets and borrowing, this is what got Louis XVI into trouble. His minister Necker produced a public report, the celebrated Compte rendu au Roi suggesting that current borrowing was sustainable, but it really amounted to "we can borrow enough to pay expenses this year", rather than "the nation can repay debts as they come due". In a hard currency world, France was insolvent, but they didn't actually see it coming, hence the calling of the Estates General to raise taxes, and ultimately the French Revolution. The Compte rendu was thus both an important step in organized discussion of national finances, and also disastrously misleading.

At present there are many alternatives to GDP as a measure of wealth suggested, for example the "Green GDP", but this is contemporary political economy, not history.

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Sources

"National Income, 1929-1932" [1934]

GDP: A Brief but Affectionate History [2015] -- authoritative academic source. The first place to look on this issue.

Lombard Street: A Description of the Money Market [1873]

The Information Master: Jean-Baptiste Colbert's Secret State Intelligence System [book is 2009, describing the economic management activities of Colbert in the 17th century]

Structure and Profitability of Royal Finance in the Viceroyalty of the Río de la Plata in 1790 -- a look at Spanish wealth in the Americas, gives an understanding of what data was being collected and how it was being used, and how the gold and silver being mined were upstreamed to the colonial metropole.

Central Bank Gold Reserves An historical perspective since 1845

Herodotus on Babylon

The Banker Who Brought Down the Old Regime: Rediscovering Jacques Necker

Mismeasuring Our Lives: Why GDP Doesn't Add Up -- critique as it says, by Nobel laureates Joseph Stiglitz and Amartya Sen, and Jean-Paul Fitoussi.