Absolutely classic symptoms/cause of flooding. That won't throw any fault codes, and if left long enough will 'cure' itself.
If you catch it quick enough, then cranking it with the throttle wide open will probably start it. My preference is not to mess about, but pull the fuel pump fuse, and while the battery is still strong crank it as above several times, replace the fuse and continue the procedure until it does start. If the plugs are nearing the end of their life, this can take a few tries. In a really bad case you'll need to remove them and dry the fuel off them; the gas stove is good for this, or a butane soldering torch. Replacing them is probably a good idea anyway.
Starting it, then turning it off straightaway 'floods' it because it is still running rich due to the cold start. If it doesn't fire on the first few turns, the plugs get too wet with fuel and don't fire. Then it's a vicious circle of more fuel making the problem worse. This can get so bad that you wash the oil from the bores, and it will sound like it has no compression.
So, I don't think you need to buy anything. But I would recommend that you leave the car running whilst opening the gate. If that means removing the gatekey from your car keyring then do it. Your ignition barrel will last longer that way too, so it's two improvements for the price of one.