Augustus
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You can also argue that science would have progressed quicker than it did. Curiosity was what was behind discovery and people would have been curious without religion holding them back as already having the answers.
You can argue that as it is ultimately unknowable, but we do have a lot of human societies to compare.
Many societies progressed technologically, but not necessarily scientifically (and many had worldviews that were not even really compatible with scientific progress as they saw the world as essentially chaotic).
People have curiosity about practical matters that impact their lives. For people to have curiosity, as well as the time and resources to ponder the unproductive pursuit of "knowledge for the sake of knowledge" and for this pursuit to bee seen as socially prestigious.
Technology can always get funding if it shows utility, but modern experimental science was mocked in the 17th C as people "measuring the weight of air", there is even a land in Gulliver's Travels (Lagado) which is basically mocking such people for living in their ivory towers and being so detached from the reality of everyday folks.
The pursuit of knowledge was traditionally only open to a narrow social elite who had others to labour for them (slaves, serfs or subjects). In most societies, social elites were also military elites and favoured martial pursuits over the pursuit of knowledge.
The funding of such research was based on patronage, and was thus capricious. When times got tougher, funding disappeared.
Something like the Church created a wealthy organisation, with many educated workers from a variety of social classes, with a fair amount of free time. These people (generally) had no military obligations, access to lots of scientific literature (which they preserved and spread), and a stable financial environment. The linking of "useless" abstract information with theological concerns gave it social prestige, and thus attracted further sources of funding.
The development of modern science was not simply a result of curiosity, but was contingent on a combination of ideological, social, economic and institutional factors.
Of course, these could have been produced by non-religious means, but the vast majority of human societies didn't produce them at all. As a result, I don't really see why we should consider the religious factors in the societies where they did emerge (and that appear to have contributed to these) as "holding them back" or assume that a non-religious society should produce them more quickly.
(I know you didn't specifically argue they would have, it seems to be a common assumption by many others though)