- The location the device was turned on, used, turned off.
- The devices contacted by the burner phone
The kind of graph databases the government uses can round down the number of people that could be using any burner phone to a reasonable guess after just the first power on and contact (call/text). This is possible with only metadata. If you have the persons voice and message content it's even easier. As the phone stays on and contacts multiple numbers the graph database increasingly narrows down the possible user. I would guess within 3 calls/texts (not considering location data, or god-forbid other smartphone data) you would have 99%+ certainty who the user was if those interactions follow any previously known pattern.
You can't hide.