I don't think there is a cut and dried answer to this; but my experience from a Montessori background is closer to write, but still not that either.
The difficulty with learning to write them is that writing is hard physically, the fine motor motions are difficult to make at that age.
In a Montessori environment, the Sandpaper Letters are the way they introduce letters. Note that they don't introduce them too early - 3 might be earlier than some would (the lesson I linked to said 4).
The idea of sandpaper letters is that you have physical letters that you can trace and feel - with sandpaper, or felt, or similar - but still on paper, not plastic cutouts or whatnot. You then say the sound of the letter ("buh", "duh", "guh", etc.) while tracing it with your finger. (Montessori prefers to teach sounds, not letter names, first, as that is the more important element of the letter, and avoids some confusing names like "double-u" or "aitch" or "gee" which don't really sound too much like their most common sound). And yes, the letters really are made from sandpaper cut out and pasted onto blocks of wood.
Here you're learning both, basically: you're learning to identify the letter while also learning in a physical sense. I (not an educator) always felt that this makes sense in the same way your write the quotation 100 times does - you experience it in multiple ways, particularly physical ways, to help reinforce the learning. That's one of the principles of Montessori learning - focusing on physically experiencing everything, math, letters, etc. - to effectively learn it.
You also focus on learning a few at a time - I like the suggestions of the link a bit below that you start with a few common letters plus the letters in the child's name, and do only 3 at a time until she's mastered those.
After that they then start working with the letters in the moveable alphabet, which is essentially similar to having alphabet magnets on your fridge.
Here's a good explanation of how to teach sandpaper letters, and a link to make them yourself also.