I have come across the claim repreatedly online and in many publications that Puritans and Calvinists believed that material wealth was how one could recognise devine favour. See here for one such claim by u/jupchurch97. However, despite it seeming universally accepted I have never come across a single mention of this concept in actual Puritan sources. Indeed some Puritan sources I have come across seem to blatantly contradict this idea. In Pilgrims progress for example wealth always seems to be a temptation. Was this actually a Puritan idea? If so in what actual Puritan sources is it discussed? If it was not an actual Puritan idea how did it become so attached to them?
The idea that Puritans celebrated wealth seems to be a slight misunderstanding of sociologist Max Weber's 1905 book The Protestant Ethic and the Spirit of Capitalism. Weber's argument is that certain forms of Protestantism are conductive to the emergence of capitalism; they have a "Protestant work ethic." He spends considerable time looking at Calvinists (the Puritans were a group of Calvinists) as an example.
Weber tried to trace back this ethic to Calvinist theology. He maintained that Calvinists could never be sure if they were part of the elect, those predestined by God to be saved. To prove that they were part of the elect they tried to live devout, almost ascetic, lives. Calvinists did not have religious orders of monks or nuns like Roman Catholics did, so the most faithful people showed their piety by working hard at secular jobs. Because their faith frowned on luxuries and they worried that an overabundance of charity encouraged vice in the poor, the most devout Calvinists had little to spend money on.
Weber claims that this meant Calvinists saved large amounts of money. Ultimately that money got reinvested, funding the rise of capitalism. Though society secularized and the religious underpinnings of the Protestant ethic disappeared the ethic itself continued to be influential.
To be clear, the argument is not that Calvinists viewed salvation as directly connected with wealth. It's that they viewed hard work and frugality as tied with salvation, and luxury as tied to sin. This happened to lead to wealth, but that was the byproduct rather than the goal.
Whether Weber is right is still a contentious issue, and it has been fought about by scholars for over a hundred years. There are critiques from the political left and right. I've always been a bit skeptical myself, in part because different religious groups, including Arminians (who rejected predestination) and Jews, were no less frugal or hardworking while having very different kinds of theology.