Before really diving into the details of Nestor's Повѣсть времѧньныхъ лѣтъ (lit. Tale of Bygone Times, but usually translated from Old Eastern Slavic as The Russian Primary Chronicle), this answer to a question from u/x_Machiavelli_x I worked on about a month ago with u/Platypuskeeper discusses the general content and overall reliability of the Chronicle for those unacquainted with what u/Nomsheep is asking about here.

In short, as OP rightly points out, Nestor's Chronicle is really the only extent source of the origins of the Kieven Rus' and is primarily used to support the Norman position in the Norman/anti-Norman debate. For those unfamiliar, the details of that debate concern whether or not the early eastern Slavs were in fact ruled by Northmen from Scandinavia or organized into some kind of exclusively Slavic demesne.

The TL;DR answer is that Nestor's position in favor of the Norman debate-- not that he was participating in such a debate-- (that is, that early eastern Slavs were ruled by Scandinavians) is generally considered to be accurate and is supported by archaeological evidence, such as the discovery of weaponry crafted using Scandinavian techniques, and jewelry worn by Scandinavian elites in and around the area Nestor attests was ruled by the figure Rurik and his two brothers. Also, there are Scandinavian runic markings at Lake Ladoga (modern Leningrad Oblast in northwest Russia, but site of the viking-era civilization now referred to as Staroladozh) indicating that someone was there with a knowledge of that writing. There are other similar physical artifacts as well stored in the Staroladozh Historical Architectural and Archaeological Museum and Archive.

Anne Stalsberg wrote an article called Scandinavian relations with Northwestern Russia during the Viking age: The archaeological evidence in 1982 which is a great source for exploring this claim from an academic perspective. Therefore, we can confidently hypothesize and support that Nestor's general claims regarding the origins of the Kieven Rus' can be trusted and corroborated.

The long answer is that while there is certainly physical evidence of Scandinavian elites living (and probably ruling) in the area where Nestor claims they did, it's quite unlikely that the manner in which they came to power occurred in the way Nestor describes. I don't want to reinvent the wheel here, because u/Platypuskeeper really put it down in that thread I mentioned before, so allow me to just excerpt a bit of their very excellent writing:

"We don't have any direct evidence of a Nestor's Rurik beyond the chronicle. However there's no obvious reason why he'd make one up either. As opposed to the actual narrative of them being invited to rule, which as said has a sensible rationale as being a justification for why a handful of foreigners were entitled to rule. If the Rus' weren't foreigners it doesn't make much sense to invent such an origin for them and a rather condescending story to justify it. Also, if we take the origins part of Nestor's account as true, then it's unsurprising and entirely consistent with history as we know it that some Scandinavian traders would emerge as an urban elite in these trading towns that were emerging together with the trade. The Scandinavian influence on these settlements is well documented. (rather randomly here's an example of a building excavated at Staraya Ladoga) Conversely, the Scandinavians picked up building techniques from Slavs, namely the building of log houses, which was introduced into Scandinavia around the 9th or 10th century and became the dominant technique in Sweden, Norway and Finland from around the 12th century until the 20th. (the remains of a log house in Hedeby has also been taken as evidence there were some Slavic inhabitants in the town early on)"

Likewise, with respect to Rurik's patrimony, I wrote this is that same thread:

"[The Varangians] ruled over Slavs. [This resulted in] the formation of the kingdom of Novgorod. Novgorod is the same kingdom Rurik's supposed great-grandson Vladimir (now Saint Vladimir) Christianized 100 years later.

But are we sure that Vladimir was truly a descendant of Rurik? The Chronicle isn't the only source for that claim, but it is the main one. Here is the supposed lineage:

• Rurik
• Ingvar (Slavified as Igor) of Kiev
• Sviatoslav I of Kiev
• Vladimir the Great

So four generations back to Rurik. One doesn't have to suspend a ton of disbelief to think that Nestor was able to access sources to support that claim, even if they no longer exist today.

Just to throw a monkey wrench into the conversation and show (again) why this is still a matter of debate:

"Igor' [is] soundly attested, presumably with dates, by the treaties with the Greeks in which [he is] mentioned by name. The chronicler could thus work back from these treaties and attach the subjects of tradition, wherever possible, to a related item of Greek chronology. Regarding Igor' he had no material apart from the fact that he was Rurik's son." (pp. 34 of the Introduction written by the translators and editors of the text in 1953, emphasis mine)

So, apparently it's not just an open and shut case as some would have you believe. Indeed, the source for Rurik's existence is only the claim of the second person in that chronology above, Ingvar or Igor. It gets worse. Igor is attested to have ruled for 31 years (914-945) by Nestor, but the treaties mentioned above with the Byzantines as well as the Chronicles itself make no mention of specific deeds of Igor until the 940's. Also from the Introduction:

"In the reign of Igor', the Varangian Russes are again distinguished from Polyanians, Slovene, and Krivichians (anno 944), and once more, in the treaty of 945, a list of names is supplied of which the majority are not Slavic, but Norse" (pp. 40)

So now we're trusting the guy who may not have even ruled for the years Nestor claims. That means that we have a historical document which makes a then-common but now-debunked claim about the inheritance of European and other lands by a person called Japheth, followed by a shaky claim about a figure called Rurik who consolidated and ruled Novgorod, which is only supported by his son-- whose own history is also a matter of debate."

(Translation of the Chronicle which includes the introduction from which I'm excerpting above)

As I imply, and u/Platypuskeeper shows quite conclusively as well, while the Chronicle is most likely quite correct in the broad strokes--i.e. we can trust Nestor's claim that some kind of Scandinavian elite came to rule over the early lands of Rus' but more likely than not, he embellishes the actual details quite significantly-- perhaps a character such as Rurik even existed, but it's quite unlikely that early eastern Slavs simply invited he and his brothers to come rule over vast tracts of Slavic land. Whether Nestor made these extrapolations based on then-extent sources (either documentary or human) or his own personal bias is also still a matter of debate.