How do you get a chicken without it coming from an egg, or in this case, how are you fascinated by this girl by more than appearance if you haven't gotten to know her somewhat already?

If you know enough about someone to be fascinated by them then you've already got a basis for speaking to them.

Otherwise a large part of the fascination is manufactured fantasy, fun to enjoy but unrelated to that person.

It might help you or us if you explained what you find fascinating about her. At the moment it simply sounds like a young man (or woman, I never assume these days) with a classic and principally hormonal infatuation with a young woman. Nothing wrong with that, per se, but as long as that is the known extent of it everyone's basically limited to offering you the regular advice, which isn't even regular introduction advice but regular life advice which applies to everything. Relax, be yourself, just do it, don't hesitate, strike while the iron's hot, etc. Everyone also views this as a regular normal thing of growing up, which requires occasional failure so from our perspective there is no negative outcome to you simply going up and talking to her, at least not one that won't be nearly inevitable in the future with some other gal.

Thus far, while saying and implying there's more to it then a normal crush, you haven't actually given the audience any justification for that.

As to social awkwardness, that is not a built in trait nor its reverse, being charismatic is something you can actually learn. Step 1 is to pretty much smile all the time. It is easy and very effective, everything else takes practice but it is a learned skill not an inborn trait.