We always tend to show that there is a link between the archaeological discoveries and ancient religious facts, especially in countries such as Egypt, Israel and other parts of the world.
Archeology is about man-made entities and human activities in history. Religious connection is only part of it ---- there are non-religious connections. Very early human activities do not involve (there was not yet a religion) religion at all.
As religion is an activity of the human being (we could say that it is a result of his agency), human agency and action usually have material manifestations: the beliefs could generate the creation of monuments (votive, funerary, cultual), and ritual usually requires (specific) artefacts and spaces. So, Archaeology can detect not the veracity of religious facts, but the belief of humans in that veracity through its material expression. That is my opinion.
The archaeologist studies objects and cultural remains within the context in which they are unearthed. This may lead to an understanding of the specific religious beliefs of an ethnic group or culture. The historian interprets texts that may provide information about the nature of the specific religious beliefs within a culture. When archaeological and historical research methods can be combined the picture becomes clearer as is the case in Egypt.
The same is true regarding the quest to extract information about a given society and its history.
As in any other field of study that interprets source material, there is no 'carved-in-stone' accuracy. To find facts about a culture long gone, you have to evaluate the methods used in each field as well as examine the conclusions. In addition, you have to investigate each researcher's possible convictions and intentions.
I agree that it's important, and indeed critical, to have an understanding of each researcher's possible convictions and intentions. But it is also very important to understand your own potential intentional biases as well.
Your own position, James, that "We always tend to show that there is a link between the archaeological discoveries and ancient religious facts", is simply wrong and misleading.
Firstly, there are no established "ancient religious facts". There are only beliefs about what ancient religious texts may be saying. And if a researcher holds a particular position on the what those beliefs were, then that can often colour how they interpret the archaeological evidence, for or against. Points of dispute in recent times include the 'James' ossuary and whether there is archaeological evidence that the Israelites worshipped a goddess as well as there one god in the early course of their religion.
The same apples to all academic fields. In my own field of Medieval Arthurian Literature, at one time it was popular to try and attribute the legends to ancient Celtic myths. Others have argued for an adaptation of Classical Greek and Roman myths. And some have even sought to trace the core of the legends back to the Sarmatians, through Sarmatian Auxillary Roman troops stationed in Roman Britain.
I concur with Kathleen, D. Toohey, but only add the emphasis that Yes, archaeology is a science. Historians, geographers, religious community, sociologist.anthropologists, and social scientists in general feed global philosophers with their findings which are are used by policy makers in governments, health sector, agriculture and politicians derive their governance components basing on them, not including other stakeholders, from the international community such as human rights groups, and academic researchers. Tourism is another area of interest in archaeologists' works.