Do any amphibians start their lives on land?
From wiki:


  Most amphibians lay their eggs in water and have aquatic larvae that undergo metamorphosis to become terrestrial adults


This suggests clearly that not all of them do so.

Here are a few interesting cases I could think of:


The common midwife toad carry the eggs on their back. The eggs are not necessarily submerged by water then.
To my knowledge, the Seepage salamander have terrestrial larvae but they don't feed before they reach the adult age.
The lungless salamanders has a larval stage that is within the egg. When the egg hatches, the individual that comes out is already an adult.