I can’t speak for every ancient faith but as far as I’m aware, other than what we call The Pyramid Texts, The Book of the Dead, and the Coffin Texts, no significant texts pertaining to Ancient Egyptian religion have survived. And for the common person this wouldn’t have been an issue. Most were not literate and participated in religion through offerings at shrines and temples and participating in celebrations where a cult statue was taken once a year from one place to another for various reasons. Basically they practiced religion as their parents and ancestors had done, and if you weren’t part of the temple as a priest then worship seemed highly personal.

Women would sometimes have tattoos on their thighs of Tawaret or more frequently Bes for protection in childbirth. Offerings of food, incense, oil, and wine were left at shrines. If you were privileged enough to have access to some passage of the Book of Coming Forth by Day (what we call the Book of the Dead) then it may be inscribed on your tomb walls or painted on your sarcophagus or simply a scroll placed in the mummy bindings.

Now, there are “hymns” from the Amarna period that have survived, and excerpts of other texts have been brought to light as well. But nothing of real significance that sheds light on actual practices. The apocryphal Book of Thoth goes back to ancient times but we have no solid evidence of it, except fragmentary notes of conversation between a mortal man and one known as The-one-who-loves-knowledge. However, this dates from the Ptolemaic period and could perhaps have Greek influence (the Greeks equated Thoth with Hermes, creating the deity Hermes Trismagistus), rather than being a truly original Egyptian piece.

Not for the "Vikings".* In the case of the Vikings this is because 1) they didn't really have or need a literary tradition like the Roman and Greek world did and 2) the belief system of the Norsemen did not form a unified body of beliefs that everyone shared.

1. Norsemen traded their stories orally, and while not entirely illiterate there was really no need to write them down. E.g. the modern view is that the reason runestones were raised is that a fair number of people could at the time actually read them, though often containing deeper meaning to those more versed in the metaphors. Furthermore, the truth is what stories we do have from them are written down centuries later by Christians who interpreted what old stories remained through their Christian Scandinavian viewpoint of the medieval period. This is important to keep in mind when we consider all the old sagas. There is precious little direct evidence of what the people in the Scandinavian countries actually thought at the time. We know the stories aren't all later fabrication though because we can see allusions to these stories on archaeological material, primarily runestones (though even runestones belong to the last parts of the so called Viking age many are even raised by Christians, and are geographically fairly specific, in that most runestones remaining come from the Mälardalen area).
2. This ties into the above. The Noresemen were not a culture monoblock. Various parts had different ideas of who the top god was and would trade oral stories/history based on their locality, which means you don't really need a large shared Big Book of How Things are (tm). Archaeology shows different places venerated gods differently, e.g. some would honour Oden as top dog (the site of Uppåkra seems to been a Oden place), others Thor and others yet Freyr, in old Uppsala all three if we believe Adam of Bremen. Some argue that what we today call Asa worship is the beliefs of the societal elites, who were also those who eventually wrote down the sagas, Oden as a wargod being more pertinent to an elite warrior class. The idea is that we can see the merging of various beliefs in that there are two types of god, the Asir (power & wargods) and Vanir (fertility gods) that the sagas warred and the Vanir then were taken in by the Asir. Some gods have linguistic and archaeological evidence of worship but they aren't recorded in the remaining sagas. This supports the idea that we only have part of the old religious and mythological corpus survive. E.g. what we think we know of the old Uppsala temple comes from Adam of Bremen, who describes it in terms of the old Roman gods to explain it to his audience of learned Europeans. Older historiography would much more uncritically take the old sagas and chronicles, their limited understanding of archaeological remains (the burial mounds in Uppsala) and marry them to 19th century romanticism to invent a past. E.g. the idea of old Uppsala with a great temple as a centre of worship for all Norsemen, like they do in the tv series Vikings. That is not to say old Uppsala wasn't an important centre for power and worship, it was. And recently, about 4-5 years ago, during an excavation to move a road they found remains of an extensive row of upright timbers in both a north-south and east-west configuration that seems to have formed a previously unknown part of the area of worship. I hope there are more extensive excavations of a site in southern Sweden, Uppåkra, that was an important centre in this period that later disappeared. If we are going to expand our knowledge of the religious practices of the Norsemen unfortunately it's mostly in archaeology our hope lies.

In short, no there is no one definitive text for '"Viking" belief' because there existed no one '"Viking" belief'. And we know very little of it.

Kristina Ekero Eriksson writes a very nice book on Old Uppsala: Gamla Uppsala : människor och makter i högarnas skugga (2018) I don't know if it exists in an English translation.

• and I always feel like nitpicking this, viking is a job, not an ethnicity per se, it comes from a verb. But it is an annoyingly handy descriptor to use.