This will be coming in the future. Please note, live streaming is extremely expensive to host and provide, so we are looking at ways to properly do this. YouTube and Facebook offer this for free because of how big they are and don't care about the costs, which puts Rumble at a disadvantage for live streaming.
I'd be very interested in some kind of live stream option as I do that regularly on that "other" platform. I do stream through obs, so I'd be happy with any solution that allows me to make a permanent switch.