How can I connect my soundbar to a TV without an optical output?

I recently bought a soundbar but didn't realize my TV doesn't have an optical output. My soundbar features aux, coaxial, and optical ports, while the TV has a headphone jack labeled "Headphones." Could I use an aux cable to connect the soundbar to the TV? Would the sound quality suffer compared to using an optical cable? I also don't quite understand how to use coaxial for this connection. Should I just return this soundbar and get one that has an HDMI port instead, or should I give the aux or coaxial connections a shot? Thanks for your help!