This question is asked in Shi'urei Rav Meshulam Dovid Soloveitchik, Zevachim 9b, by Rav Dovid shlit'a, the Rosh Yeshiva of Brisk in Yerushalayim.

1) He cites the Gemara in Bechoros 4b that many Korbanos were brought on the day that the Mishkan was set up (Rosh Chodesh Nisan). Rav Dovid says that one of these Korbanos was the calf of Aharon for a Chatas, and the Pashtus is that these Korbanos were brought before the Korban of Nachshon, so why does Rashi write that the one of Nachshon was the first Chatas Yachid?!

2) Rav Dovid answers that the reason might be because of what it says in Sifri Zuta 7:11, which states as follows: "Moshe said to them, 'It has been said to me that you should all bring Korbanos, but it has not been said to me which one of you should bring the Korban first.' They all looked at Nachshon and said, 'He was the one who did a Kidush Hash-m for ha'Kadosh Baruch Hu at the Sea, so he is worthy to cause the Shechinah to come down.'"

3) Rav Dovid says that it appears that when the Sifri Zuta says that Nachshon is worthy to bring down the Shechinah, this means that the fire from Shamayim came down to receive the Korban of Nachshon. This seems to prove that the Korban of Nachshon was the first one offered.

4) Rav Dovid concludes by saying that this issue requires further elucidation ("Tzarich Iyun").

Kol Tuv,

Dovid Bloom

Here are additional insights on the Peshat in Rashi:

1) First, I should note that what I cited above in the name of Sifri Zuta is in fact found also in Midrash Rabah, Parshas Naso, end of Parshah 12, so it is quite easily available for everyone to see.

2) There is a very interesting note in Gilyonei ha'Shas, by Rav Yosef Engel zt'l, on Shabbos 21b, in the Sugya of Chanukah. He talks about the famous question of why a Nes was needed to make the Tahor oil in the Beis ha'Mikdash last for eight days, when the Halachah says that Tum'ah Hutrah b'Tzibur? They could have used any Tamei oil for lighting!

To this well-known Kashya, the Gilyonei ha'Shas answers based on a Yesod as follows. The first time ever that a Mitzvah is done, it must be done in a way that is a Mitzvah Min ha'Muvchar, and it is not enough that it is done in a way that is only Kosher Min ha'Din. The Gilyonei ha'Shas brings an example of this from Parshas Shemini. After Nadav and Avihu died, why did Moshe Rabeinu tell Misha'el and Eltzafan to remove the bodies of Nadav and Avihu from the Heichal, and not Elazar and Itamar?Elazar and Itamar were ordinary Kohanim who, unlike a Kohen Gadol, are allowed to become Tamei for their brothers!

The Da'as Zekenim mi'Ba'alei Tosfos (Vayikra 10:3) answers that even an ordinary Kohen -- on the first day that he begins performing the Avodah in the Beis ha'Mikdash -- has the status of a Kohen Godol and therefore is not allowed to touch even his brother who has died.

This idea also answers the question of why it was not sufficient to rely on Tum'ah Hutrah b'Tzibur after the Beis ha'Mikdash was regained from the Greeks. This was the first time that they had been able to offer Korbanos in the Beis ha'Mikdash for over 50 years, and they made a special Chanukas Beis ha'Mikdash and therefore required totally pure oil, which is why Hashem made a miracle for them.

The Gilyonei ha'Shas then cites Rashi here in Zevachim 9b (DH Ikar). Rashi adds the interesting word that the Korban of Nachshon was the "root" of the Chatas. According to the Yesod of the Gilyonei ha'Shas, we can understand this better. The first time one brings a Chatas, it must be with all of the right Kavanos, becames it sets the way for all of the Chata'os that will be brought afterwards.

3) This is why Nachshon was the one who had to bring the first Chatas. As the Midrash says, the reason he brought it first was because he made a Kidush Hashem by jumping into the Yam Suf first. The Peshat is that the whole Inyan of bringing a Korban is Mesirus Nefesh. A Korban is a Hakravah, a sacrifice, that takes the place of offering one's own self, as the Ramban writes (Vayikra 1:9) that a person who brings a Korban should think that what is being done to the Korban should really have been done to him as a punishment for his Aveiros.

4) This is how we know that the Korban of Nachshon was the first one offered on Rosh Chodesh Nisan. He was the one who had the most Mesirus Nefesh, and this is why he was the right one to start off all of the Korbanos that were brought in the Mishkan.

Kol Tuv,

Dovid Bloom