Can't send itunes music from iphone 13 to a dac with lightning connector

The charging cable that came with my iphone 13 has a usb-c male connector that plugs into the iphone and a lightning connector on the other end that plugs into the charger. I am trying to connect my iphone to a digital to analog converter(dac) that has a lightning input so I can play itunes music on my stereo system. This supplied charging cable will connect the two devices but, when connected, no music signals are getting to the dac. I understand this charging cable may not have been designed carry audio. I was led to believe an Apple USB-C to Lightning Adapter(part no. BOCHX5RZ8M) would resolve the problem so I ordered one only to find that it was actually a Lightning to USB-C adapter. The male connector on this adapter is lightning and the female connector is USB-C which is the opposite of what I need. It seems to me that all I need is a cable like the charging cable that came with the iphone that will handle audio signals but it is unclear to me which available cables will actually work. I appreciate any help you can offer.