How do hot air balloons get started (without burning the fabric)?
The balloon is spread out on the ground and rigged to the basket.
Then, a cold air blower is used to do the initial inflation, blowing air into the envelope through the bottom aperture. This gets the balloon about 75% inflated, but still horizontal.
Lastly, the burners are lit to heat the cold air already inside the canopy, expanding it and raising the balloon to vertical and full inflation.

You can find any number of videos on YouTube that show the process. Here's one: