After create a Live Event, Can we get a join link from API as response?

Hello,
A live event is not a conferencing event. It's an ingest entity. Once you created a live event, you need to start it and then you can get the input endpoint with a GET. This input endpoint accepts RTMP (or Smooth) stream coming from an encoder. This input URL must be configured in your live encoder to push the live stream to Azure Media Services.
To distribute or record the live stream, you also need to create a live output.

Adding to Xavier.

I assume by "join link" you may have just meant the manifest to use in your player to playback the live content?

One easy flow is to create the Live Output entity attached to an Asset up front, before you start the live event.
I then create a Streaming URL on the Asset ahead of time as well, to share with the player before the event begins.

Once the live event is up and running, and you see content in the preview endpoint, you can then start the Live Output.

Think of live outputs as "recording machines" and Assets as "tapes to put into the recording machines".

Create the recording machine up front, start the live event, start your RTMP encoder. When ready to shut down, stop the Live Output first (this is a DELETE call), and then you can use the content in the Asset for streaming as VOD instantly (same Streaming URL).
You can then stop the Live Event itself to shut the resources down and stop billing.