What Sonos devices do you own? If you have a Move or Roam, you can connect your phone to the Move or Roam over Bluetooth and play the podcasts from Acast.

If you have an iOS device, you can play the podcasts over AirPlay to any AirPlay-enabled Sonos device. Read more about AirPlay and Sonos here:
https://support.sonos.com/s/article/1230?language=en_US

Currently have 1 Sonos One and 1 One SL, using Android devices.

I don’t see Acast as a partner for Sonos, unfortunately, so you may be restricted to many of the suggestions above (although the line-in connection directly to your phone isn’t mentioned), but in the meantime, you could petition the folks at Acast by suggesting that they go look at the Sonos partners page and become a partner. 

Along with what @Airgetlam posted, you can also check and see if the podcasts you listen to on Acast are available on any of the streaming services Sonos actually supports.