>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 a preposition can license a gerund as opposed to *to infinitives* or other class of verbs.( Perhaps it is close to a noun or nounlike.). 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. Preposition ***to*** cannot license this form of verb.


But ***start*** is a noun if preceded by a determiner like *the* and takes an *of phrase complement* as exemplified in Andrew Leach's example.

>He's looking forward to the start of his job next week.