No, you can’t rule out the battery cables or a bad battery for that matter.
concerns me. Does this mean the battery, engine off is showing 12.6 volts? Or charges TO 12.6 volts on a charger? If so, the battery would seem to be OK. If this is the voltage you get when the car is running, the alternator is likely bad since that number should be about 14.5 volt when the battery is charging.
The cables may be able to carry enough current to run the lights or that connection is from separate wire. The cable to the starter may be bad or the starter itself may be bad. Check the voltage at the battery with the ignition turned to the start position. Does the voltage drop to about 9 volts with no click? Likely bad starter. Drop way below 9 volts? Likely bad battery (a surface charge is fooling you). Check the grounds and the main positive to the starter. Check for voltage at the starter. Remove it and check for resistance and corrosion. First places to start before removing the starter and having it checked.