This sounds like the classic standard problem with small Kubotas (and Deere, and others.) First of course check your battery condition AND clean all the terminals and the ground at the chassis too. Assuming the problem persists it is almost certainly the voltage drop from the battery to the solenoid (slight voltage drops in every safety which leaves marginal voltage by the time it gets to the solenoid. That's the underlying problem.)
Do this: 1) Try hooking a battery charger, not a jump start battery, to your battery. See if it will start while the charger is connected. [What happens is the charger puts out put MORE voltage than a jumper battery, around 13.8v instead of 12v, and often that overcomes the voltage drop in series through all the dern safety interlocks. 2) If the charger works you can operate in that nuisance mode for a while [I did that for month or two in 2023 on a
BX2200] but that is not a permanent fix. 3) To confirm the issue, run a heavy jumper cable from the positive batt terminal to the large output wire of the solenoid which is the input to the starter. Turning the key with that solid connection would start it. Actually I suggest
having someone else hold the key into the start position with the clicking going on
while you do the jumper. Not sure what happens in the other order.
4) Longer term permanent solution is that the Kubota dealers around here sell a "hard start kit" which means a new relay that is triggered by the normal small wire from the start switch circuit but runs the direct battery voltage to the solenoid bypassing the safeties. The safety features are still preserved since the small wire runs in series through all those.
Deere dealers sell the kits too and it is the same stuff.
You will find MANY threads here in TBN describing this problem and solution.