Paul is employing the rhetorical device of the royal "we"! After all, he was himself a Jew, wasn't he? Furthermore, the term "Jews" itself isn't used in Rom 3:9! However, the inference you make is correct, since Paul himself was a Jew and is using "we" in the royal sense, which I will now prove by adding additional context.
The fact that he was not directly addressing the Jews can also be seen in 3:1-3,which reads:
Rom 3:1-3
3:1 What advantage then hath the Jew? or what profit is there of circumcision?
Notice he didn't say "what advantage then hath YOU Jews. Here he's asking a question about "the Jew".
2 Much every way: chiefly, because that unto them were committed the oracles of God.
"Them" in the above text is a third person pronoun. A very odd pronoun to use if Paul had been directly addressing Jews. If he was addressing them directly, he would have used a second person pronoun, instead of a third person pronoun that speaks about rather than to them!
3 For what if some [Jews] did not believe? shall their unbelief make the faith of God without effect?
KJV
Here again, we have the identical situation as in the previous verses. Paul did not say, "what if some of YOU Jews did not or do not believe? And part "b" of the verse strongly clinches this fact with another third person pronoun "their". Paul did not say, "shall YOUR unbelief make the faith of God without effect?" Plus he could have never said that since he was in fact writing to believers!
One of the chief hermeneutical errors that so many believers commit when interpreting scripture is that we fail to take ourselves out of our present, 21st century circumstances and modern culture, which are thousands of years removed from the actual historical context that will be accompanied, invariably, with useless, unnecessary and damaging presuppositions, and instead consciously place ourselves into the shoes of the ancient original audience to see how they would have understood the ancient writer. We often fail to ask two extremely important questions: What did the ancient writer mean and how would his original audience have understood him? By failing to consciously adopt these highly and critically important hermeneutical principles for ourselves every time we approach the Word of God, we will almost inevitably be led far astray and misunderstand the passage under consideration. (A large passage that immediately comes to mind and is very often handled in the most irresponsible and careless manner possible is the Mount Olivet Discourse. If we students of God's Word would only place ourselves into Jesus' original first century audience (which in this case would be in the shoes of Peter, John, James and Andrew (Mk 13:3), we could never in a million years embrace the serious eschatological errors proffered by Dispensationalism and even other schools of eschatology. But I digress...Back to the immediate subject at hand.)
So...I implore you to personally adopt these two critically important hermeneutical principles and place yourself into Paul's original audience in the church in Rome. First, Paul was most defintely writing to believers (Rom 1:7). But what kind of believers: Jews, Gentiles or a mixed bag of both? Verse 11 answers this importan question to wit:
Rom 1:13
13 I do not want you to be unaware, brothers, that I planned many times to come to you (but have been prevented from doing so until now) in order that I might [currently] have a harvest among you, just as I have had among the OTHER Gentiles [in the past].
NIV
Key Takeaways from the above verse:
1. Paul confirms he's addressing saints with the term "brothers".
2. Paul addreses these saints directly by using the second person personal pronoun "you" twice.
3. Lastly, Paul unmistakably and irrefutably addresses these "brothers" as being Gentile believers because he considered them to also be Gentiles.
So...do this: Pretend you're part of Paul's original audience and you're a Jewish believer. Would you not be insulted by Paul writing to YOU, thinking that you are another Gentile believer? Paul must have been thinking that or esle why would he consider you to be just like one of his Gentile believers to whom he ministered in the past? The term "other" makes absolutely no sense unless the apostle considered his original audience [you] to be just another Gentile audience to whom he is currently minstering through his letter.
Was Paul confused regarding the identity of his original audience? Or are you confused?
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