Our Gemara on Amud Aleph tells us in regard to identifying that the verse is referring to an Esrog:
GEMARA: The Sages taught that the verse states: “Fruit of a beautiful tree,” meaning, a tree that the taste of its tree trunk and the taste of its fruit are alike. What tree is that? You must say it is the esrog tree.
There is a beautiful Zohar (I:220b) on this which interprets the function of the triad of Yamim Tovim in Tishrei: Rosh Hashana, Yom Kippur and Succos. I will try to explain it to the best of my ability, based on Sod Yesharim (Succos 34).
The Zohar wonders why the Torah refers to taking the four species on Succos as taking on the “first day”. “First day for what?”, wonders the Zohar. “It is compared to a king who kept his subjects locked away and then his mother asked him to set them free, which he did under her care. Once set free, they needed food and water, which she took responsibility for, asking the king to Still provide for their needs even though they were set free from the Palace grounds.”
Ok, so here goes the nimshal and it’s intense. Rosh Hashana Represents God alone on his throne, before or right at the moment of creation. Nothing is differentiated; everything is all Him, inchoate and singular. This is represented in the non-verbal sound of the shofar. There are no words because everything is a singularity, just God and His truth with no differentiation or mediation. Then we have Yom Kippur. Now, mankind enters the scene, still not released onto the world but a distinct entity. This is represented by the verbal prayers of the Yom Kippur service. Speech, by its very essence is “I, thou” and dialogic. It implies talking to someone, so that means there are two entities. Finally comes Succos, when humankind, like the servants in the mashal, are finally released to live in the world.
But they need food and drink and they need to be sustained. On Succos the Shekhina makes sure we are provided for now that we exist separately and left the compound of the king.
The fact that the Esrog is a unique fruit, whose taste, that is the aroma, pervades the wood as well as the fruit, is reminiscent of the state of perfect Edenic care that God provides. The alternative fruit, considered by the Gemara but ultimately rejected was the pepper. Though pepper also has its taste pervade its wood, it is not the ideal because it is only a seasoning, not an actual food. This represents failed and imperfect attempts to derive heavenly sustenance.
So to summarize: Rosh Hashana, Yom Kippur and then Succos follow a progression. Initially God is alone and absolutely undifferentiated, represented in the non-verbal sound of the Shofar. Then humankind appears, but is not yet fully separate and so expresses itself verbally in the prayers of Yom Kippur but has no need to eat, as humans are not yet fully in the physical world. Succos is really the “First Day” of life in this world, according to this Zohar, when man needs sustenance from God, represented by the Esrog and the Harvest.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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