This certainly sounds like the starter or the circuity. Reason is, when you pop the clutch and it starts, all you are doing is using the weight of the car to do the job of the starter to turn the engine over. All else needs to be functioning (ignition, spark, fuel) in order for this to work.
I thought maybe the crank sensor was the issue but again, this doesn't make sense because the crank sensor tells the PCM when to fire the plugs and injectors. If it didn't have that then it won't have started when you popped the clutch.
Unfortunately, now that it is functioning it will pass all the tests. However, I included the test for the starter solenoid if it does act up again. You need to get power to the solenoid in order for it to click. If you have a connection issue, you may not get it to click and this would cause intermittent operation. It won't hurt anything if you want to unhook the battery (both terminals) and then clean the battery terminals and then unhook the starter connections and clean them as well. Then reconnect the battery.
Just take notice if any of the starter connections are loose or do not look like clean metal. If they are not, that could be your issue.
Let me know what you find and I will be happy to assist further.
Images (Click to enlarge)
Friday, September 11th, 2020 AT 4:15 PM