Your uterus starts moving up after your first trimester, you can be bloated and what not before hand but this isn't actually your baby showing. From 16 weeks onwards you're more likely to develop a 'bump' the farther along, the higher your uterus plus the bigger your baby. Some women don't show until 34 weeks, some even 38!
Each person differs so you shouldn't wait for certain week when baby starts growing. :) Your doctor will tell you about signs in each phase.