Question Connecting wired headphones to a new TV

Nov 2, 2019
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Hi,
I have a pair of really good wired headphones I use to listen to music on my phone. To do that I connect them using FiiO K3 - an USB-C DAC/amp. Everything works great.
Recently I bought a new TV, where the playback device is Nvidia Shield TV - the new 2019 non pro version, that does not have any USB ports. The question is - how in god's name do I connect my headphones to this setup ?
No headphone jack on the TV, no USB ports on the Shield to use as a source for the DAC, and the USB ports on the TV don't provide an audio signal. There is optical audio output on the TV and HDMI with ARC, but that cannot power my DAC even if I bought a HDMI-USB-C cable. I'm out of ideas. I did not really want to buy more components, but it seems unavoidable. What would be the cheapest alternative?