Yes! Here's how:
In your room, click your avatar on the bottom of the page to open up Settings, or on the top right of every page, you can click your avatar and select Settings from the dropdown menu.
This will launch a tabbed SETTINGS window. Select the second tab, Audio/Video. Options to start with your camera and microphone off on are at the bottom.
Check these settings to start with your microphone/camera off and uncheck them to also start with your mic and camera turned on.
These options are currently unavailable on mobile.