i wonder what country you are in. i feel like there is 90 days return here (but maybe its a California thing?) anyway repairing the screen from a local repair shop is not a acceptable outcome for me as they don't ever use the same quality screens (if they can help it). I have learned from my own mistakes and reading these posts over and over about not testing a new item and then worrying about the warranty 3 years later. the Op did purchase from a shakey site if they have since gone down (online has grown not shrank right?) you mention you bought the phone from "the retailer" what store was that?- Nearly the exact same thing happened to me with a Pixel 3a phone I purchased for my wife's birthday.
Bought it a month in advance from the retailer. She opens it up, loves it, goes to go through the set-up... dead screen. Retailer says its outside of the two week in store return policy, so now I have to go through Google. Luckily they authorize a repair on the phone from a local repair shop, but it now has a 90 day refurb warranty, not the 1 year new manufacturer warranty.
Granted the phone has worked for over a year at this point without issue, but this whole incident reminded me why I actually like buying used parts: they're confirmed working and you tend to actually get more buyer protections through something like e-bay and paypal than you do buying something new through a retailer.
Can read my saga here: https://forums.anandtech.com/threads/pixel-4-for-499-or-pixel-3a-for-399.2580078/