No ancient community that I know of was ever secular in the modern sense, by which I think you mean that most people either did not have an organized faith or religious beliefs, and religious belief was disconnected from any socio-political choices that community made. In the ancient world, this is simply not the case, at least as far as my knowledge goes, which is mostly limited to a deeper understanding of the Mediterranean from the 2nd to 1st millennium BCE, with some knowledge to the east of the Mediterranean and maybe a millennium before and after this time period.

Religion was, however, very different. We have some understanding that no religion was as organized as missionary religions are today; in the Late Bronze Age for example, while the Hittite Empire had a myriad of priestly officials, no one stood over the other in matters of religion, and local cities (such as Emar in the Middle Euphrates) that the Hittites conquered (which is a loaded term which needs to be unpacked separately) had their own religious officials in many cases (Matthew Ritz’ book on the Diviners of Late Bronze Age Emar is a detailed description of one of these phenomena). There is no understanding of any of these religions having the equivalent of the modern Catholic Pope, for example.

Moreover, the important seemed to be placed on orthoxpraxy rather than orthodoxy, as many modern religions are. What this essentially means is that people were concerned with an individual in the community upholding the right practices to be considered an upstanding part of that faith community. There is never any text I know of, in Akkadian, Greek, Hittite, Luwian, Latin, or any other ancient language that I know of where someone genuinely is trying to convince another person that a divinity exists in a specific form. In fact, many ancient religions were very good at religious syncretism, that is, looking at other people’s faith practices and beliefs and understanding those practices and beliefs in relation to what they understand about the world. For example, when the Greeks encountered the Phoenician religion they seemingly did not find any of it incredibly strange except a number of practices. They were very willing to equate some of the Phoenician gods to their own; Melqart was Herakles, Eshmun was Asklepios, etc (The Oxford Handbook to the Phoenician and Punic World has some good introductory chapters on this). So, to belong to a faith community in this region, one really didn’t have to believe anything, one only had to participate.

This is not to say nobody believed the gods existed and simply went through the traditional motions; far from it. It was seemingly assumed on the part of most people that the gods existed and there was no need to argue that or explain it. Because of this emphasis on practice, many religions in the ancient world were far less organized, and practice varied at the local level. Phoenician religion, what we know about it anyways, is a good example of this. While most gods were assumed to have exist by almost everyone in a Phoenician city, each city had its own triad of gods it explicitly connected with itself and its urban community; the patron god of Tyre was Melqart, of Byblos, a manifestation of Baal. However, none of these cities did the exact same rituals with the exact same temples, and practice varied at the local level. When the Phoenicians spread west, particularly to Carthage, another set of practices developed there, particularly around child sacrifice (Quinn’s 2018 book “In Search of the Phoenicians, chapter 5 on the Tophet is a good introduction).

All this is to say that while we have no examples of secularism, or areligious communities from the ancient world, what counted as religious practice was slightly different to ancient people, and much of their faith practices might be viewed as “less religious” by modern people than, say, an emphasis on conversion and belief which we see in some Abrahamic religions. But it is clear that religion permeated life back then.