Cisco video conference

The mute/unmute on the device itself will be independent of the mute/unmute within the Zoom meeting unless you have the Cisco device managed through the Enhanced Room Connector and Registered to Zoom via SIP enabled:

https://support.zoom.us/hc/en-us/articles/360052154312-Enhanced-Zoom-Connector-for-SIP-H-323-devices

We use Polycom Group presence series Video conference hardware to connect to Zoom and with that device you need to engage the onscreen menu with the Polycom remote by clicking #1 and then 2 unmutes and mutes the mic. since the device joins as a participant you could also join as a host on a laptop or tablet and then request to unmute the mic on Cisco, you should see an onscreen request to unmute. 

I know this is late, but i thought i would chime in to update the thread.
I also have Cisco gear, the issue is Zoom's SIP service does not connect the device functions. So when the Host has set MUTE ON ENTRY, you will have to use the dial tone controls like Dan Huber mentioned. There is a set of Macros you can install that help with this function but Cisco is rolling out built in Zoom controls in the next CE rollout.