One big click usually means a problem within the starter assembly; either the contactor that the solenoid is closing or the starter brushes, or the armature windings. Winding issues rarely "self-heal", so likely one of the other two. Reading voltage at that big stud on the solenoid with the short strap/cable going inside the starter case will tell if the solenoid contacts are the problem. Just a solenoid can be replaced, and sometimes the contacts can be rotate 180 degrees to "renew" them enough for quite a bit more use.
If the problem is low voltage to the other big stud on the solenoid, from bad battery/cables/connections, then that usually shows up as a continuous "click-click-click..." What happens is the battery/circuit is good enough to power the solenoid coil and pull it in, making a click, then the starter contacts "make" and the starter motor puts a heavy load on the circuit. So, voltage to the solenoid then drops so low that the coil can't hold the contacts together. They open, the heavy load goes away, voltage is again good enough to pull the solenoid in and make contact, then the whole cycle repeats... click-click-clik