At first glance it appears that CD player has a Bur Brown 1704 DAC which was state of the art when it first came out , albeit many many audiophile moons ago. Regardless I can only image Esoteric went full tilt on the implementation and its a good place to start with a DAC.
The default answer for people starting out here is Bluesound Node. But if you want to explore a high end option take a look at the Bryston BDP-3. It will stream Tidal and Qobuz and go Coax out to your Esoteric. It also supports DSD files. There is a BDP-3 on audiogon now for $2.2K. New they are $3.6K I think.
The Lumin products also get mush love on this site. You might include the Lumin U1 in your exploration.
Note, Do you have wired Ethernet to your rig or only WiFi?