Is 1 week too soon to give up trying?

I (M15) have been very attracted to a girl (F15) at my school (UK) for the past week but have honestly had no hope in speaking to her. When at school we are in form and 1 class both of which we sit no where near each other and have nothing to talk about while walking to or from class to start conversation. Even when I do manage a chance to start a conversation her closest friend is usually with her and quite dislikes me so it feels really weird.

I have her snapchat and instagram but she only uses her phone every few days and almost never checks her messages so it's likely that the message i sent her yesterday asking if she would like to go out for food at the weekend won't be seen for a while if at all. I'm also shorter than her and not that popular so I honestly don't have much going for me but genuinely really like her. We've had conversations ranging from a couple of seconds up to a half hour in the past and it flows quite well and I can make her laugh but it seems too difficult at the moment.

I'm not sure if it's genuinely not going to work or if I'm just being impatient.