Is it normal for a level 2 character to have a +8 attack modifier?

One of my player’s character is an archer elf with a +4 Dexterity modifier. When she uses her longbow, she gets the +2 poficiency bonus, plus the +2 bonus given by her archer specialization. That gives us a +8 modifier on the attacks with the longbow. Is it normal ?

On one hand I’m a bit surprised because it seems high, but on the other I feel it would be unfair to nerf it.

I didn’t find where to look for the answer, can somebody help me ?