Yes, it is possible!! Though it requires the use of an Amazon Firestick.
I recently picked up a second-hand Hisense Roku TV and had the same question. Like you, I wasn't satisfied with the "not possible" answer, so I did a bunch of trial-and-error testing until I came across a setup that I was satisfied with.
The first step is to setup Alexa Home Theater mode on a Firestick or FireTV device, instructions here:
https://www.amazon.com/gp/help/customer/display.html?nodeId=GENPVVD63RZMN7CU
Not all Echo devices are compatible with all FireTV devices, so make sure you're working with the same-generation devices. For example, a Firestick 4k 2nd gen will work with Echo Dot 4th gen speakers, but won't work with Echo Dot 3rd gen (but Firestick 4k 1st gen will).
Not sure why they couldn't make all their devices work together, but here's a compatibility list:
https://www.amazon.com/gp/help/customer/display.html?nodeId=GYYMWGZJUK28FEN6
Once you've got the Alexa Home Theater mode working, the rest is fairly simple. Go to the audio settings on your Roku TV and manually set the audio to output to the HDMI(ARC) device for your Firestick.
Audio output worked immediately on my TV, but the volume buttons weren't working until I powered the TV off and back on again. Now audio for the TV comes out the Echo Dot speakers and both the Amazon & Hisense remotes are able to control the volume. Every so often it gets glitchy, where audio still works but changing the volume with the remote stops working, but power-cycling the TV fixes it.
Hopefully that helps. 🙂