Fan odour

A lot of ac shops use an ozone generator inside the car with the ac running to kill bacteria in the evaporator and ducting, it is fairly common.

'Some one's' put a kipper in your air plenum...(don't ask me how I know hehe)

If you always use recycle mode then you are never making fresh air travel through the evaporator, cool bit and making the problem worse and worse. That dries you out too and makes you less alert especially in hot weather.
Try spraying GLEN 20 into the entry to the recirc system under the glove box. The Glen 20 even kills horrible odours/smells left from school students on long overnight 24 hr interstate trips in busses/coaches. We used to use it regularly to kill influenza/colds and those horrible odours created by humans. It works. I wonder what Toyota do, they probably don't flush it as such, just administer some bug killer. Glen 20 is cheap and always keep a can in the vehicle. "Simples".

Too much RECIRC is NOT healthy for anyone.
Just an after thought, if the AC drain is blocked and not draining, irrespective of being new or not, it would retain moisture to STEW while parked and cause bugs to grow. When the aircon is running does the water drips from inside LHF wheel/beside engine happen as normal???? Maybe a wasp has built a nest in the short drain hose facing downward..
Turning off the AC before stopping or leaving it active will not make a scrap of difference to your problem cause.

I have a mate who bought a fairly new hilux a few years back off a private seller.
The seller was a smoker and somehow hid the smell of cigarettes in the car unbeknown to my friend.
Sadly once bought he realised his problem.
Long story short of it is.
Car detailers can get rid of the smell as well as in the ac ducts these days.
Ask around
No idea on cost.
But i certainly couldn't pick it.
And i hate cigarettes! !

As its happening more when not on recycle (or on fresh air), it sounds like you have either had something die down the grill in the air intake or a cat may have peed in there. I have had both happen and it is not pleasant. Neighbours cat took up to peeing on my windscreen for some reason and the smell coming in the vents was horrendous. I ended up trapping it, but that's another story.
Try giving the inlet a good flush with a hose, making sure the drains are not blocked. you may find a frog, lizard and just debris rotting on there. It doesn't hurt to give the inlet and drains a good flush every now and again to make sure they are draining.
Tony

Is it a chemical smell, you only need a slight amount of coolant seepage to cause quite a stink in the car. I have this with a KIA, doesn't use any water but each time you turn the heater on there is stink of coolant for 30 seconds or so. Has done it ever since I have had the car.

The fact that the smell goes away with the AC on without recycle or with no AC and recycle points to it being carried in water vapour external to the heat exchanger as it appears condensing the water vapour with the AC on removes the smell. This points to what others have suggested of something wet and rotting upstream of the heat exchanger and recirculate 'baffle'.

Brent, there's a product called Nilodor which is very effective at removing smells, even animal urine smells.

I would have to agree that the cat piss scenario is quite likely, cats are very curious and will get into garages even through small openings.
I've often found cat paw prints on our garaged car, on the bonnet, and on top of the doors, along the ledge at the bottom of the side windows - and we don't own a cat.

Rodents are also notorious for pissing on things, and it could even be a dead mouse in the bulkhead vent area.

Nilodor reviews

Cheers, Ron.

Try turning off the a/c a minute or two before you shut the car down will usually reduce the odour you'll get next time you start the car.

Not sure of the reasons, but I think this warms the heat exchanger reducing condensation prior to shutting down the car, and dries out remaining condensation in the exchanger. Leaving the a/c on until you shut down the car leaves the heat exchanger very cold and subject to condensation and when the fan stops, there is no air moving past it to dry the condensation, and therefore you get water that sits in your a/c system, potentially going 'bad'.