Get the markings off the chip right next to it. Looks like a Realtek ALC(nnn) audio chip. With the chip markings you can often find the Realtek datasheet showing the chip pinout.
It may be an audio signal coupling cap and now missing, may have caused loss of a channel of audio. Whether you need that channel, among the multiple channels it has, you'll have to test to determine. Remember to also test input, not just output channels.
I hate these dark motherboards for circuit tracing but if you can figure out which chip pin the capacitor was going to, using the datasheet you can better determine if it was for an audio channel, or might instead be a power supply decoupling cap which could prevent stable operation or make it noisy.
Anyone good at soldering "might" be able to fix that, unless it tore off the PCB solder pad right next to the chip, then trying to connect that to the miniscule trace going to a chip pin... a bit more advanced microsurgery with a microscope would be needed (labor cost exceeds board value).
Ultimately, it's not going to hurt anything to power up the board and test audio functionality, and if a necessary feature is compromised, might be cheaper to just throw a sound card into the system or USB connected, if the alternative was to pay someone for a repair. It would probably result in better (analog) sound quality too, the chip is "okay" but the implementation with ceramic coupling caps and proximity to the board ground plane (and no voltage regulation I saw so not an isolated power supply feed) is far from the optimal implementation, rather done that way for minimum PCB real estate taken and cost.