You're focusing or zooming in on an element appearing in field of view. Think in terms of eyes or camera, and time one spends reading the text as time spent looking at the object, and pace the description accordingly.
If you walk into a room, and the middle is occupied by an elephant, and you approached from its front, delaying the shock at seeing an elephant will be completely misplaced.
On the other hand, as you observe a silhouette coming out from morning mist, you will resolve details gradually, as they become visible.
Nevertheless, "something" is a terrible placeholder for an out-of-focus object. If she was hard to see at first, you can give "a silhouette". If she was well visible, "a girl" or at least "someone". Unless you were stumbling in pitch darkness, you saw thousands of "somethings" and another one really doesn't help.
In your situation, you need about as much time as one takes to read "I caught sight of a girl." to catch sight of a girl standing nearby in bright sunlight when you emerge from behind a curve, so the second approach is right. Now if it was dusk, fog, and she lay huddled under a bush, you might go for the first description, possibly adding approaching and peering through the gloom.
Simply, pace exposure matching speed of reading to speed of focusing on the elements of the scene as if it was for real. Obvious, clearly visible object - immediate focus. Fine detail - huddled at the end of the description. Approaching a hard-to-see object - start with vague and solidify as details become visible. Passing in a blur - just a blurry hint of shape. Vision impaired - perception impaired. Need a second or two to evaluate what/whom you actually see - paragraph break. And match that first glance impression to what you actually see at a first glance. Reserve "something" for severely impaired sight.
(I don't really like the second option you give. "As I came out of it..." would be better, "once" seems to imply the curve took quite some time and effort.)