Beard is synthesizing a ton of material so perhaps she’s on to something or is obliquely referring to an established argument, but she doesn’t expand on her claims or cite them, so I hope someone can fill me in. In her opinion, leading Romans of the early republic didn’t know or at least didn’t think about Rome’s physical place in the world and were instead concerned with relationships. Is there any reason to view the Roman republic as in some meaningful sense lacking a cartographic / geographical awareness? Seems like a strange and wrong claim but maybe I’m missing something...
It’s been a long time since I read SPQR so I don’t have that specific point right in front of me and, moreover, the early republic is really a period I have largely ignored (I’m basically of the opinion that we basically can’t know anything about the early history or Rome before say the early 3rd century outside of the broadest of strokes).
That being said, I think that point is largely accurate. Rome of the early Republic (so pre Punic Wars era) is a very different world from even the Rome of the end of the century when the overseas adventurism was beginning with the Macedonian Wars and Scipio’s victory at Zama. And this Rome still pales in comparison to the Rome of Cicero’s time, which was less sophisticated still than the Rome of the principate.
Basically what I’m saying is when talking about early Rome we really need to imagine a very different world from what we tend to imagine Rome as, which is largely constructed from later periods (and later periods that likewise had sometimes very significant differences between them too).
And this is without getting into the additional problem of our sources, from whom we get our narratives and overall picture are likewise almost all written well after the events in question, From Livy writing Rome’s mythic history, to Polybius telling the story of Rome’s rise post hoc when Rome had become a superpower, which means it comes across like a sure thing when it was anything but.
So in sum, I think it is probably correct to view early Romans as essentially parochial, which is how I read “pre-cartographic.” They were isolated on their peninsula. If there is any semblance of truth in the first decade of Livy (I’m generally skeptical, but the broad strokes are probably still have some connection to reality), then Rome spent several hundred years embroiled in the kinds of regular, seasonal city-state wars as was typical in Greece.
Rome ultimately brought a good portion of Italy under its suzerainty, but Italy wasn’t ever truly incorporated until after the Social War in the first century. Additionally, it wasn’t until the first Punic War that Rome really did much off of Italy proper and actually raised a navy. Rome was in its own little world, until external events drew Rome out. (Well kind of, the reasons for Roman imperial adventurism beginning in the 3rd century is complicated and beyond the scope of this question)
While this is by no means central to the question here – on which I can't really comment as I've not read SPQR – I just want to flag up a potential misconception underlying your question.
We know next to nothing about the scale of Roman 'map-making', as no fragment of any Greek or Roman world map survives. What is more, our knowledge of what they may have looked like is equally vague, though we can reasonably suppose that even into the empire there were some significant gaps in their geographical knowledge beyond the scope of their imperial ambitions. On this, see my previous answer about Roman maps and Scotland.