Were Celestia and Luna born Earth Ponies?

Question

I ask because Twilight Sparkle was born a Unicorn, and Cadance was born a Pegasus. Also, only Flurry Heart was confirmed to be born an Alicorn.

Answer 1

The “Unconfirned” (at this time) Answer

The other answers are great and well-reasoned speculation, but the birth-status of Celestia and Luna is something which has not yet been detailed.

Adding to the speculation, Alicorns can be either made or born (although, this could also be a meaningless distinction as “made” comprises “born” as a sub-category). But the distinction is valuable in noting the various alicorns for purpose of additional speculation, from Wiki:

• Twilight, born unicorn (female)
• Cadence, born pegasus (female)
• Flurry Heart, born alicorn (female). Gameloft Mobile game adds the qualifier “First alicorn baby in all time and space. But…)
• So Soft Newborn Princess Skyla (female), technically not quite sure whether she became an alicorn upon/after birth, or was born an alicorn. For Gameloft to be correct, Princess Skyla would have to have been born something else and became an alicorn while still being a “newborn” but not a “baby” — an unlikely proposition but perhaps not impossible given flexibility in definitions of both “newborn” vs. “baby.” Standard definitions of “newborn” cover the time of birth usually through hospital discharge, but there is no quantitative limit beyond qualitative “recently born” status; likewise there is no hard and fast rule when one stops being a “baby.” This condition would be easier to fit were the terms reversed (I.e. Gameloft using “newborn” and So Soft using “baby,” but alas we’re stuck with what we have.)
• Cozy Glow (female), born pegasus
• Sunny Starscout (female), born Earth pony

An interesting commonality is that every known alicorn is female, suggesting that while race plays no role in establishing a pony as an alicorn, sex may.

As both Celestia and Luna are mares, this interesting observation plays no role in their being alicorns. They may have been born Earth ponies, but we don’t know.

If Celestia and Luna were born alicorns, however, it would break Gameloft’s canon regarding Flurry Heart being “the first alicorn baby in all space and time.” So for completists seeking to fit Gameloft, it’s unlikely they may have been born alicorns. Or for the even more esoteric completists, they may have been born Earth ponies and became alicorns, like Skyla may have such that they are somehow “newborn alicorns,” but not “baby alicorns.”

Other Outliers

• Queen Chrysalis was introduced as “gnarly, black Pegacorn” in script for A Canterlot Wedding - Pt. 1 but it was later established that the chrysali were a wholly different race than Earth ponies, unicorns, and pegasuses.
• Princess Erroria (female): An interesting example of “nature vs. nurture” question: Erroria was erroneously drawn as an alicorn in Twilight’s & Sweetie Belle’s imaginations (one wonders how different Erroria’s life might have been if she was instead named “Correctia?”)
• unnamed Alicorn drawing (female): from the book that the Cutie Mark Crusaders read in Hearts and Hooves Day

Answer 2

In this interview, Lauren Faust, creator of My Little Pony Friendship is Magic, indicates that Princess Celestia embodies the traits of Earth Ponies, Pegasus', and Unicorns. I'm guessing the same applies to her younger sister, Princess Luna, who was also alluded to in this statement:

Color has never, ever been depicted as a race indicator for the ponies. When your characters are purple, blue, orange, yellow, black, white, red, green and pink, who’s to say which is supposed to signify a white person, a black person, an Asian person? The only races in My Little Pony are Earth Pony, Pegasus and Unicorn, and they are all treated equally, ruled by a leader who embodies the traits of all three. This leader is white only to signify day, and she co-rules with her sister, who is purple to signify night. Additionally, I’d just like to assure anyone who might still question the guards at the foot of the Princess’s throne that their colors were picked arbitrarily–and they are paid for their service.

This is backed up by trading cards that list their pony type as Pegasus, Unicorn and Earth:

Their type has also been listed as Alicorn in trading cards:

Answer 3

Adding to the other answer, the Journal of the Two Sisters actually narrates how Celestia and Luna came to be princess.

After the three tribes of Earth Ponies, Pegasi and Unicorns came to an agreement, Star Swirl came to them for a specific reason

“They knew that Alicorns stood for everything Equestria was founded upon: love, harmony, and friendship. And because Alicorns are a combination of Pegasi, Unicorn, and Earth ponies, they believed that we could represent the citizens of Equestria in an unbiased manner......so they asked us to be their princesses.”

This passage confirms that the two sisters were already Alicorn at the time, and that should be enough to assume they were Alicorn since birth for at least two reasons:

1. Celestia states in the main show that "a natural born Alicorn is something that didn't happen for a long time" when Flurry is born, meaning that it did happen before. Considering their longevity, you would think that any Alicorn born after them would still be around during the show main time period.
2. It is quite improbable that they ascended to Alicorn status alone before meeting Star Swirl since they didn't had a tutor, couldn't control their magic very well and probably lacked friends. Compare to what Twilight went thru.

The Journal was considered canon by the original show writers, including Amy Rogers. So that is probably very close to the original intended plot.

.... but there is a problem. The latter writers managed to meddle with the script and as a result the events of the book are somehow incompatible with the later added plotline about the seven pillar the last show seasons introduce.

So, basically, it is quite clear that they were at least originally intended to be natural born Alicorn, but the final seasons kinda destroyed some of the lore that enforced that idea.