Get the orderbook depth snapshot via websocket API?

Is it possible to build the full orderbook ONLY using the websocket API?

In other words, can I get the initial depth snapshot using the websocket API?

No, it is not possible to receive a snapshot via WebSocket Streams alone.

You should use /api/v3/depth REST API endpoint to get a depth snapshot, then apply updates from the <symbol>@depth stream to it. That is the fastest way to get your local order book in sync.