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I would return the phone back. It happened to me once when I bought a brand new iPhone 6s Plus in 2018 November. The model was selling Brand new in U.K. up to 2019 from many vendors like Amazon, Argos etc.

I bought three devices two 128gb (one from Giffgaff and one from Amazon) and one 32gb from Amazon for my mother. The first one from giffgaff came with depleted battery. It took few minutes to start charging.

I am checking all the batteries for new devices and old ones with cocconut battery. It shows me also the date of manufacturing of the batteries.

The 32gb was the best unit, recently manufactured battery, perfect screen and the battery still holds strong.

My first giffgaff battery was the worst. It charged 100 but through the years the battery capacity fell quickly. The manufacturer date of the battery was very old as well. The Amazon 128gb came with almost depleted battery and 1 year fresher battery. Both these phones has a small defect on the screen. The battery on the second 128gb phone hold charge a bit better not perfect though. I attribute this behaviour for both phones to the old age of battery manufacture. I have replaced both these batteries with new ones from Apple for 49£ After two years of use.

I believe that these 128gb phones where an old batch with some defects that were sold in a big discount so I am not really complaining for both the old batteries or the screen. I would not though accept a fully depleted battery for an expensive new iPhone according to my experience.

Is very difficult for the battery Health for iPhone to show below 80. Even when my coconut battery shows 75 capacity the iPhone never falls below 80 so I do not trust it completely.

However I think the 49£ fee is a fair fee for new battery replacement and thus I have changed 5 times batteries for 4 6s plus phones in general (one for free with the Apple program )
 
I would return the phone back.

I did just that. I was in the mall and decided to stop by the Apple Store to ask them about this. They said that it was definitely not normal for a brand-new iPhone 13 Pro to have totally depleted battery out of the box. Although, they couldn't find anything really wrong with the phone when they played with it.

To my surprise, they said they had another iPhone 13 Pro 256gb gold in stock. Someone had apparently cancelled the store pick-up order a few days ago. She asked me if I wanted to go home and bring the box back so they could exchange it. Unfortunately, I live almost 80 miles away.

They couldn't just let me return the iPhone 13 Pro without a box. I ended up buying the one they had. They opened it in the store and the battery meter showed 72% right after I logged in with my Apple ID and activated it

Yesterday, I shipped back the first iPhone 13 Pro via FedEx. The new one appears to function just fine as of right now. :)
 
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