To benefit from your low distortion DAC, you need a low distortion generator. Less trivial than it seems.
You didn't mention what kind of signal you want to generate? Pure sine? Other waveforms?
There are pretty expensive units, such as this:
https://www.nti-audio.com/en/products/digirator-dr2(Probably not worth it if all you want is to reuse your DAC.)
As others have suggested, a PC/ or SBC-based solution is probably your best bet for a simple and low-cost approach, yet with the ability of generating low-distortion signals. If you have access to I2S signals on your DAC, you may not even need an additional SPDIF board (some SBCs have I2S built-in).
You could also do this with a microcontroller or an FPGA, but there will be significant dev time, especially if you want some kind of UI.