The fact that Snorri Sturlason was a Christian is not generally considered to be very relevant. The intent of Snorri's Edda was to promote the writing of Old Norse poetry. It includes folklore stories about the gods for the purpose of explaining the older poetry known in his day, and to serve as background material for the composition of new works. There's not much reason to think Snorri intentionally distorted anything; although it's plausible (at least) that he added some guesses and elaborations in trying to reconcile various accounts. And his belief in Christianity certainly colored his perceptions, and the fact that the society around him had been converted for centuries and continued to tell this folklore and invent new stories in that period, has to be taken into account. Some stories about the pagan gods were most likely composed in the Christian era.

But that's the thing, it was a living storytelling tradition. Not religious scripture. Neither Snorri or other medieval Scandinavians seem to have been particularly interested in documenting the actual beliefs and rituals of his forebears. Snorri doesn't really say whether people believed in Valhalla, or to what extent they did. It's dubious whether he'd know that anyway; Snorri never met a pagan. Iceland had converted upwards of two centuries before his day.

So the problem here is not that anyone (anyone of consequence anyway) believes Snorri invented Valhalla as a Norse analogue to Christian Heaven. In fact we can be quite certain he didn't, as the name and concept appears repeatedly in several poems of the Elder Edda (Völuspá, Grímnismál) as well as Skaldic poetry (Hákonarmál), and these do date back to the Viking Age. We know mainly on linguistic grounds; poetry is typically conserved well as it's difficult to change words without screwing up the meter and so on, and the meter itself also makes it easier to memorize verbatim. In any case, the language of these poems is archaic and they're centuries older than when they were written down.

But none of these, at least not in the form we have them, are older than contact with Christianity. Nor older than when missionaries began arriving in Scandinavia in the 9th century.

We know from material culture for starters, that contact with Christianity lead to new influence, such as the wearing of Thor's hammer pendants (starting around the 9th century) as a kind of reaction to the Christian cross. (whether reaction in-opposition-to or in-imitation-of, or whichever..)

Some archaeologists (e.g. Anders Andrén) would even consider Christian influences to go as far back as the 4th and 5th centuries.

Perhaps Roman sources regarding Germanic religions?

There isn't that much. Mainly Tacitus, who is not a primary source, very vague and sketchy and incorrect in many of the details that are specific enough to actually test.

But the Romans are 800-1000 years before Snorri. Why would it have anything to do with it? There's a problematic (but often held) assumption underlying this, which is that pre-Christian Norse religion was somehow representative of a single "Germanic" religion that was by-and-large static over time. Although this was commonly assumed at one time, today it's considered largely debunked; we know religious customs were quite heterogenous (even within Viking Age Scandinavia alone) and we know they changed over time. Prior to Christian influences there were Roman ones, both from Greco-Roman mythology and from Mithraism.

To quote the aforementioned Andrén:

The old idea that Norse religion somehow represents an archaic and unchanging tradition on the periphery of Europe can thus no longer be maintained.

And on whether or not Christianity influenced the depictions of medieval Scandinavians' like Snorri and Saxo Grammaticus, he says:

In either case, the authors of the 13th century created new hybrid forms, which in their own way were merely a continuation of the hybrids that had been created earlier.

(Anders Andrén, Behind Heathendom: Archaeological Studies of Old Norse Religion, Scottish Archaeological Journal Vol.27(2) 105-138, 2008)

So in short, yes, the idea that Valhalla is a Christian influence is something that's seriously entertained, even if's not thought Snorri invented it.

Then there's another matter, namely whether the Valhalla concept represents was an actual widespread religious belief about the afterlife, or whether it was merely a literary trope of Norse stories. As /u/Steelcan909 says in an answer here (also /u/y_sengaku has a good post or two on this I couldn't find on short notice), we simply do not know whether or not sincere Valhalla-belief existed at all. In fact we know very little about the actual rituals and belief system here.