>He is looking forward to starting his job next week.


***To*** there is a preposition that normally requires a noun as its complement. It can also take a **gerund** (verb+ing) because ***starting***(gerund) has noun properties. Still, it's a **verb** and that's the reason why it can take **"his job"** as its own object.  

>He is looking forward to start his job next week.

This one is ungrammatical. **Start** is a verb and doesn't have noun properties like ***starting.***