Yes. We still identify ourselves with them, we have a direct mesorah from them, and there were shuls back then, just they weren’t central. We follow the same Torah (they learned Torah Sheba’al Peh, we have it written down), but we are at a lower madreiga then them, so Chazal composed davening for us. We are different though, as we have many cultural sects (S’fardim, Ashkenazim, Lityvaks, Chassidim, etc.), we have some new halachos (Chanuka, Purim, electricity on Shabbos, and so on), but altoghether we are the same people. Am Yisrael are unique in history.
“Anyone who calls Judaism a religion falls into the fatal error of putting it in a category”
-Rav Avigdor Miller, Sing You Righteous
We are the same Am Yisrael who saw open miracles when we left Egypt, for forty years in the desert, for over four centuries in each Bais HaMikdash, who heard Hashem speaking before over three million people from a thundering, flaming mountain, who learned and expounded His Torah and did His Mitzos for over two thousand years.
“You might inquire about times long past, going back to the time Hashem created man on earth, [exploring] one end of the heavens to the other. See if anything as great as this has ever happened, or if the like has ever been heard.
“Has any nation ever heard Hashem speaking out of the fire, as you have, and still survived?… You are the ones who have been shown, so that you will know that Hashem is the Supreme Being and there is none besides him.
“From the heavens He let you hear His voice admonishing you, and on earth he showed you His great fire, so that you heard His words from the fire”
-Dvarim 4:32-35