(so called): Did it really exist before Acts 10:45? If it did, it was fully inclusive of all believers in Christ, at that time. Or, to put that more clearly - No, it did not.
I know, depending on your translation, Luke seems to say one particular group of circumcised believers was especially stunned when the Holy Spirit fell on Cornelius. However, a major problem here is that there simply were not any uncircumcised [male] believers in Judea, at this point. For one thing, that's the entire point of Luke telling Cornelius' story! But there's more.
Here's what Acts 1-10 tells us, about conversion and gentiles:
First, the whole problem of the gentile widows in Acts 6 was their lack of having a husband, whether Jewish or Gentile, who could have been circumcised. Otherwise, where were the gentile orphan boys also being overlooked? There were none. The overlooked persons are entirely widows. As for Philip & Stephen (etc), they simply must have been circumcised. Since Peter required a vision from God (10:28) merely to cross over Cornelius' threshold (10:25) and to touch him (10:26), there's no way 'The Seven' were walking into Jerusalem's christian storehouse if they had each been unwashed and uncircumcised. (On Nicolas the proselyte, see note at bottom.) But, again, if those hungry widows had even had gentile husbands, that daily chore could have been solved once for all, with a knife!
More broadly, there's a definite pattern that forms in Judean evangelism, after the scattering. The Samaritans, every male presumably being a circumcised son of Abraham, were baptized by Philip in water, and given the Holy Spirit by Peter and John (who evidently knew more about Samaritans than did Philippos). The Ethiopian eunuch, being uncircumcisable, was baptized only in water. Last, Cornelius, upon receiving the Holy Spirit while still being uncircumcised (the astonishing part), now only has to be baptized in water. Quite consistently, each new convert required (1) baptism and (2) the Holy Spirit, but only received HS if circumcised into Judaism.
Back to Cornelius' house, where, depending on your translation in 10:45, this may not be so clear. A cursory reading of most renderings gives a definite impression that there were already two well established positions on whether circumcision was required. There's no evidence in Acts 1-10 for taking on that position. None at all. To create the appearance of such evidence, one must anachronistically rehabilitate Peter before his transformation's complete (or even begun, hardly, really).
Let's look at the scripture for Acts 10:45.
NASB says, "All the circumcised believers who came with Peter were amazed..." (Yes, but that statement would be equally true if omitting the word "circumcised".) ESV says, "the believers from among the circumcised who had come with Peter were amazed..." (Right. As opposed to which other believers?) NLT says, "The Jewish believers who came with Peter were amazed..." (What? In the context of this particular story, WHO were the "Gentile believers" standing there, unamazed, in Cornelius' house?)
The Greek, of course, says καὶ ἐξέστησαν οἱ ἐκ περιτομῆς πιστοὶ ὅσοι συνῆλθαν τῷ Πέτρῳ ὅτι καὶ ἐπὶ τὰ ἔθνη ἡ δωρεὰ τοῦ ἁγίου πνεύματος ἐκκέχυται, which being approximately transliterated, means something like "and they were amazed, those of the circumcised believers, the ones who came with Peter, that also upon the nations the gift of the holy spirit was poured out."
There are two possibilities here.
First, Luke may be putting in a deliberate allusion to Paul's phrase, τοὺς ἐκ περιτομῆς ('those of the circumcised', Gal.2:12), which Paul likely repeated elsewhere, including probably after his arrest. A few verses later in Acts, Luke uses almost the same construction at 11:2, οἱ ἐκ περιτομῆς A(same meaning), this time to reference Peter's vigorous opponents in this suddenly realized debate. This may be the same point in both verses. But if Luke is using the phrase in 10:45 to refer to the opponents of 11:2, or Gal.2:12, or anywhere in the historical middle... in other words, if Luke is referring to the oft labeled and partly mythical movement scholars long ago labeled "The Circumcision Party"... then Luke is creating a deliberate anachronism.
By deliberate anachronism, I mean something like "America's first president was commanding general in our Revolutionary War." or "I met my wife at Hartsfield International Airport". In both cases there's a chronological discrepancy, but if you know the backstory of either situation, there's no misunderstanding. This is a common enough way of speaking, efficiently adding additional information into a conveniently succinct statement.
Now, the second possibility is that Luke may have meant to refer simply to ALL the believers who were standing at that moment with Peter. As has been pointed out here, above, Luke's statement DOES in actuality refer to all such persons, anyway. Even so, it may ALSO be the case that Luke was foreshadowing 11:2 with this phrase in 10:45. Either way, this second possible view says that Luke had no intention of identifying a sub-sect which was instantly forming at this time, and certainly not one already existing prior to this time.
By all accounts, this sub-sect "of the circumcision" had pretty well started forming by the time they returned to Jerusalem... but of course that's getting things backwards. Whichever view took the early majority after Peter's return, that first sub-sect within Christianity began in Cornelius' house. Prior to that, all believers in Christ were required to be circumcised (or have circ'd husbands). All of them.
It's anachronistic to think anything other than this, about Acts 1-10.
As Peter himself said to Cornelius, up until then the procedures for gentile proselytization were internationally well known (10:35) and it had been made very clear that the way to salvation in Christ was through joining with certain Jews in Jerusalem (10:39). Yes, according to Luke that's what Peter believed, right up until that next moment. While the full meaning of God's sheet letting down and the clean/unclean talk becomes clear to a reader at this point (10:45), one of Luke's purposes in telling the story this way is to point out that not even Peter understood this before now - not after Joppa, not after initially knocking on Cornelius' door. In fact, Peter was still spouting off about what the plan was when the Spirit intervened.
And at that point, Peter, he of the circumcision, was astonished.
And the other believers, also circumcised, were astonished right along with him.
At 11:2, we've got the start of division. Maybe Luke's slight ambiguity in 10:45 is the spark of that division, but there's no evidence in Acts 1-9 to suggest there was any other opinion for how gentiles could be saved but "Circumcision". Indeed, that was how everyone in the Jerusalem church had been taught. Luke doesn't bring it up quite so early, in Acts 2, but the Day of Pentecost may have included several circumcisions of God-fearing proselytes. (Note: that double term is not a redundancy. A circumcised Gentile was also called 'proselyte'.)
That, of course, would be a Circumcision "Party" of an entirely different kind!
I'd go on to show how translators also anachronistically rehabilitate Peter's sincere question at 10:47, making it into a noble rhetorical defense of Cornelius... but this post is too long as it is. Suffice it to say that the situation was unprecedented (and perhaps also that Peter was used to communal decision making) and I'll let you all go look at the Greek and its popular renderings for yourself!