I just finished this process, so I'm writing this to share how I accomplished it.
The vehicle: a 2021 model year dealer demonstration vehicle with over 6,000 kms on it. Still considered "new" in Andorra.
I purchased it in Germany from a Fiat-Chrysler dealer (now Stellantis Group). Had the dealer expose the VAT/MwST, showing the netto price and brutto price. I paid brutto and had him add into the sales contract some language saying that upon sending them the import papers stamped from Andorra, the dealership would refund the MwST, that is the difference between the brutto and netto price.
From the dealer, I received the folllowing:
Signed sales invoice showing netto sales price and 19% MwST, original invoice for the vehicle listing all options, EU certificate of conformity, teil1 and teil2 (german vehicle registration papers), insurance purchased by dealer in my name, zoll/export papers that the dealer filed for me showing the port of intended export on the border of France and Andorra, ausfuhrkennzeichen (export license plates).
I drove toward Pas de La Casa, stopping at the shared customs building in France. Parked outside in the median a few steps before the Policia booth and walked inside the building. French Aduana is on the left. I went to the window and told the lady I wanted to export a vehicle. She scanned the barcode on the zoll/export papers, checked the computer, and said that's it, now you can go to the Andorra customs on the other side of the building.
At Andorra customs/duana, the guy at the window told me to guy upstairs so I did. I explained to the man upstairs that I just exported a vehicle from the EU and wanted to import it and get MT, matriculas temporales. He asked for my residency card and I told him I don't have residency, then he told me sorry it's impossible then, you won't be able to register it. A few days prior I had gone to the government edifice in Andorra la Vella and requested a NIA (national ID number), and I showed hiim the paperwork from that and told him I was certain they said I could register a vehicle as a tourist. He went to talk to someone, returned and said ok with your NIA we can proceed with the import. He spent 30 minutes on the computer, then came to take the payment of 4.5 percent sales tax via credit card.
After paying, we went downstairs and he talked to the guy behind the window who finalized everything and gave me a second stamped document, on top of the stamped export/import papers from upstairs.
I left. The next day I visited the ITV station to get a techinal inspection of the vehicle. Upon arriving, you first need to walk to the small office on the RIGHT side of the building. Not the door in the center. Show the lady all of the papers, the German registration, certificate of conformity, Import papers, papers showing you paid the 4.5% sales tax to Andorra, etc. She insisted that I needed Andorra insurance first but I insisted that no, the ACA of Andorra told me to get the technical inspection first, then go request an insurance policy. She consulted a colleague then relented and processed the paperwork, and gave me papers to give the guy inside the garage.
I got in the queue, and had an inspection which lasted a good 20 minutes, then got stapmed receipts. Next I went to an assegurances office that was about 1 or 1.5 blocks west of the Andorra govt building, on the opposite side of the street, and got a quote for insurance which sounded good (650 euros, full coverage in all of Europe, 200 euro deductible), agreed to the policy, and the agent printed me an insurance certificate to show the govt.
I took that along with the ITV papers and existing stack of papers back to the main government edifice and told them I was there to collect the NIA I requested, and also to register an imported vehicle. Oh by the way the aduana/customs guys looked up my NIA based on my receipt, so I didn't actually have to show them the NIA paperwork previously, just my receipt from having applied.
The lady there gave me my NIA document, then we began the arduous process of filling in the solicitud for vehicle registration/matriculacion. She had a rubric for the German paperwork that showed her what to put in each box on the solicitud, but it was still tough. In 3 days, the yellow card and my registration paperwork will be ready. At that point I can go get the license plates manufactured, pay for the insurance policy and get the insurance papers, then I think I need to go back to the ITV station with the plates on the vehicle to finalize everything.
I hope this helps someone. BTW I didnt need a telephone number in Andorra, I just used my Canadian number. For a local address I used the hotel's address.