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Answer: Tevilat keilim for the six metals mentioned in the Torah (Bamidbar 31:22) is, according to many, from the Torah (see Beit Yosef, Yoreh Deah 120). For glass, it is indeed Rabbinic (Avoda Zara 75b). Let us work with your assumptions.
Bemare Habazak - Rabbis Questions (654)
Rabbi Daniel Mann
371 - Fulfilling Kiddush from One Who Did Not Eat
372 - Toveling which Utensil First
373 - Accidentally Staying on the Bus Longer than Envisioned
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However, the issue does not apply here for two reasons. Tevilat Keilim ((Cohen) 9:(22)) points out that even when tevila is on a Torah level, the beracha is only a Rabbinic obligation. Therefore, he argues, the beracha of one doing tevila on glass can be used for one toveling metal. In truth, though, even regarding Birkat Hamazon, one who ate only enough for a Rabbinic obligation can be motzi (when there is a need) one who ate enough for a Torah-level Birkat Hamazon (Shulchan Aruch, Orach Chayim 197:4). Furthermore, in your case, the beracha applies to all of the utensils that were slated for you to tovel, not just the first one (see parallel application of this concept in Shulchan Aruch, YD 19:7). We even find that one can make a beracha directly before something that may not be a mitzva, and it can go on that which follows. An example is that while we do not know which set of tekiot are the correct one, we make the beracha before the first set and it works even if the second or third set is correct.
We can still ask whether there is at least a preference, had you thought of the issue, to have immersed the metal first, right after the beracha. We do find in regard to berachot before food that the gemara (Berachot 41a) brings rules of kedimut (precedence) – which berachot are made first, and which food should be eaten first after a given beracha. Even if one does not follow the proper order, the beracha takes effect (Magen Avraham 211:11), but we do like to do things correctly. Here, though, it is a different type of beracha – not a birkat hanehenin (on benefit, primarily food), but a beracha on a mitzva. So really the question is whether one mitzva has precedence over another.
The gemara (Zevachim 90b) does address order in mitzvot. Tadir (a more common mitzva) has priority over a less common one. Also, mekudash (a more holy mitzva) has precedence over others. What about a mitzva from the Torah over a Rabbinic one? Beit Shamai and Beit Hillel (Berachot 51b) disagree whether the beracha on wine comes before or after the beracha of Kiddush. The Sha’agat Aryeh (22) claims that the fact that pieces of logic including tadir are raised and the matter that Kiddush is essentially a mitzva from the Torah whereas the beracha over wine is not is not raised, shows that that Torah/Rabbinic obligation must not cause kedimut. On the other hand, R. Akiva Eiger (to Orach Chayim 7:1) assumes that being from the Torah is like being mekudash. The P’nei Yeshoshua (Berachot ibid.) also assumes that being from the Torah gives mitzva precedence, and explains that Kiddush over wine is usually only Rabbinic. Yabia Omer (IX, OC 100) bring several others who concur. However, I have not succeeded to find, in our context of tevillat keilim, that the utensil one puts in the mikveh first should be one that is obligated by Torah law.
In summary, it might be preferable to tovel the metal utensil first, but this is not clear in the sources, and it certainly does not make a difference after the fact.

Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
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Kuzari -Rabbi Ari Shvat Kuzari class 9 - "Seeing is Believing" (parag. 21-30)
These paragraphs elaborate on the theme that seeing and knowing is better than any attempt to prove logically, and begins explaining the difference between Israel and gentiles.

Ein Aya Various Universal Stages of the Geula Process
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Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
How do we know that the "claim" of mass revelation to 2,000,000 witnesses at Mt. Sinai is really true? This important class answers all of the questions skeptics ask about this claim of the Kuzari.

Ein Aya Armies Still Necessary for Balance & the War Against Wars
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Kuzari -Rabbi Ari Shvat Kuzari class 7 - Five Accumulative Proofs of G-d
As a preparation for the Kuzari's classic proof of G-d from the mass-revelation at Sinai, we start here with 5 other directions to strengthen our belief which also contribute to what the Kuzari will present as well.

Ein Aya Muscle & Meaning: The Dual Nature of Gevurah (Physical Strength)
Is physical strength and fitness a necessity or an ideal? Although it if often totally overlooked among topics of Judaism, Rav Kook writes that it clearly is also a necessity to deter the many enemies of Israel, but even in Y'mot HaMashiach, in the Messianic era, to a certain extent, it's ideal continues even after our enemies will have been finished off.








