You might want to read “Twilight Sparkle and the Crystal Heart Spell” and find out.

She was an orphaned pegasus who earned the Alicorn status by beating Prismia, an old mare who wore a necklace that amplified her negative feelings.
 
Thats canon in Twilight Sparkle and the Crystal Heart Spell book.  
So pegasi and unicorns can become Alicorns which begs the question: can Earth Ponies?

It’s some great fanfic fuel if you ask me. Perhaps Cadence has some long secret history.

She made that love spell.

@Amber  
perhaps because Twilight was the furthest along in the group?  
Hypothesis: that the key function of the elements of harmony is to reveal a being’s true nature. The elements attract/ are attracted to ponies of exceptional nature, ones most likely to become alicorns or who have the aptitude to do so. When functioning as one, they can trigger the apotheosis to alicorn in a subject that is ready for it.  
They aren’t the ONLY way to become an alicorn, but they’re a powerful catalyst for it.

Celestia transformed her while she was still in her mothers womb. Cadence is the last in a line of artificial Alicorns created to keep Celestia company while Luna was spaced.

@Background Pony
 
 
But if the EoH has anything to do with alicornication,why only Twilight became an alicorn?
 
Which it take us back to Cadence,I know her background story is still quite weird,but we got what we got.She’s an alicorn.And it must have been impossible for her to turn into one because of the Elements because they were inactive and far away from her before the story started,maybe even before she was even born.
 
That’s why I still believe Twilight is the first one to have achieved alicorness by other means.

Cadence didn’t earn them at all. She is to stupid to do so. Instead, Hasbro stapled them to her.

@Amber
 
I think it mentioned that their reign started after they defeated Discord, which would’ve possibly coincided with them becoming princesses, and probably alicorns as well.
 
Also the EoH seem to have something to do with alicornication, and if that was also around the same time they found the EoH…

@Background Pony
 
>SORT OF implied that Celestia and Luna became alicorns after defeating Discord.
 
Exactly where? they just said Celestia and Luna discovered the EoH to defeat him since his Reign was causing unrest to everyone.
 
It didn’t imply anything abut them becoming alicorns.At least,I don’t see any allusions to that.

… Uniforn.
 

It was never specified how old Cadance was anyway.  
Sure she grew in the 10 years or so since twilight saw her as a kid but that could have been anything happening off screen.
 
Luna in S1 also was much shorter but “grew up” in S2 and noone denies her immortality.

@Background Pony
 
Maybe that answer of what an alicorn actually is actually just an answer out of many questions surrounding them?
 
Because hey,they still didn’t explain why Celestia and Luna are immortals? why Cadence seemed to grow normally? what was Star Swirl’s goal by trying to create that spell?
 
The mystery is still there.
 
Personally,I think Celestia and Luna and Cadence were born alicorns(Cadence being a very distant relative).
 
Twilight may be the first one to “ascend” to alicornhood by using other means.

@Background Pony
 
Sure it would be nice if she had a good story behind that, but we saw her being a young alicorn so we can presume she was that way before reaching adulthood and presume she was born one.
 
Maybe you can do something about Celestia, Luna and Cadance being larger than the rest of the ponies when Twilight become an alicorn without growing to their size.

She’s a unicorn with wings. She’s a mutant who just looks like an alicorn.

@RIG  
@Amber  
That’s a disappointing answer since the season 3 finale finally gave us an answer of what an alicorn actually is.
 
I know Cadence was an alicorn because toys, but they could try to deal with the fact once it was imposed and move beyond “just because lol”.

She was born alicorn.

She made a love spell that actually worked.

@Fipse  
Yep.  
Could she be a descendant from those who ruled the crystal empire before Sombra?
 
At least we know shes related to Celestia.

You answered your own question uploader :D  
/ bronyfive

she was born as alicorn, a mortal alucorn.

She was alicorn from the beginning but haven’t reached her maximum sized in Twilight flashback.

In the words of lady Gaga. She was born this way.

Because Hasbro figured alicorn princesses sell.