Were Celestia and Luna originally unicorn who have discovered the magic of friendship in each other? Were they born alicorns? If that's the case what about parents? I don't know... Please keep this as canon as possible!
I would imagine they were born alicorns, hence their multi-millennial lifespan. Since it has been stated that Sparky will not outlive her friends, lifespans that long seem to only apply to Celestia and Luna. I think someone else brought that up in another thread and it seems to make a lot of sense.
If we are keeping things as canon as possible, then the only reliable answer is we don't know. Though, there are plenty of clues that give us an idea of what Equestria's history is like. We know that ponies came from somewhere else, before Celestia and Luna reigned, according to Hearth's Warming Eve. We know that Discord tormented the ponies of Equestria before Celestia and Luna imprisoned him using the Elements of Harmony, according to Return to Harmony part 1. We also know that this was over 1,000 years ago since it's before Luna's own imprisonment detailed in the first episode. We know that Celesita and Luna also defeated King Sombra though it wasn't stated if they used the Elements of Harmony or just used their magic, according to The Crystal Empire Part 1 They were still Alicorns in the flashback. We also know that there was a Princess who was love poisioned in the legend of Hearts and Hooves day, according to the episode of the same name. The picture in the book clearly showed an alicorn though we don't know when it was suppose to take place. The logic in the show seems to be that every alicorn is a princess, since Fluttershy says that Twilight looks like a princess when she gained wings in Magical Mystery Cure, but not every princess is an alicorn since Princess Platnium was one, being the daughter of the Unicorn King, but not an alicorn, as shown in Hearth's Warming Eve. We know that Alicorn's age, since Cadance was shown younger in Canterlot Wedding Part 1 but we don't know if Celestia and Luna are unique cases since they are at least over 1,000 years old, with no signs of aging. We also know that they are in charge of the day and night cycle, something that use to be the jobs of the unicorns according to Hearth's Warming Eve. Lastly, we don't know if Alicorns can be born or are always made. Cadance has some non-canon material stating she was a pegasus before Celesita made her an alicorn....but then there is Princess Skyla who as far as any of us are concerned is non-canon until she appears in the show. All of this is just the evidence to prove that we don't have enough information. Alicorns are pretty much a concept the show directly mentions in the final episode of the latest season and Equestria Girls was too busy talking about humans to talk about alicorns. Hopefully season 4 will give some more insight.
^^ Pretty much this, although there has been evidence in the show that makes it pretty clear that there are some pretty big loopholes in logic concerning the history, physics and plot of the show, so not only is it unknown, but unless they explicitly make it clear in the show I find it rather futile to try and logic up an answer when logic doesn't seem to apply to this case. Perhaps Mrs. Faust had a cleaerer picture of how all the jigsaw pieces fit together, perhaps she didn't. We'll never know. And unless the new writers decide to go into detail, we may never know.