Odds of Getting In
If it weren't competitive, it wouldn't be prestigious. Only about fifteen percent of elves graduating with a BE (that's Bachelor of Elving) degree are able to secure employment in the Workshop. Of those, only one in ten survive the first year. You'd have better luck working your way into a Tolkien novel.
But if you apply yourelf, are prepared to interview more than once, and walk into that tiny office with a won't-take-no-for-an-answer attitude, then you just might wriggle your way in.
However...you'll probably just have to take no for an answer. Seriously—don't argue with a hiring elf. It won't go well for you.