If the charger that came in the box with my new phone doesn’t work can I get it replaced free of charge?

Of course you can … as long as it’s determined that the cable has failed due to causes covered by the warranty and within the specified time limits.

You can review the details of your warranty here:

Find information about your warranty or AppleCare plan - Apple Support

and here:

Legal - Hardware Warranties - Apple

Of course you could under the terms of Apple’s - or of any reputable authorized reseller’s - warranty …

… but “new” Apple iPhones have not been shipped w/ power adaptors for over 3 years.

(Apple stopped including power adaptors in the box beginning w/ iPhone 11 in late 2019)

You’re welcome.

Hope you get everything working soon.