How to handle timestamps in live sources that produce data in PAUSED state

When a live source produces data in the PAUSED state, the timestamps of the first buffers are earlier than the pipeline’s base time. How to solve this problem to make sure that the generated timestamps are unique.
One possible solution to this problem is to let applications set start time and base time. Is this the recommended way?
Thank you in advance!

Live sources are only supposed to produce data in PLAYING state. You could simply drop data in PAUSED, for example, if you have no way around producing it at that point.