Yes your print head is damaged beyond repair..
There are several ways to protect your print head when using the printer, first is to start every print run with a nozzle check , and if that is clear and proper then it’s safe to proceed to print.. Otherwise run a clean cycle..
The quickest way to damage the print head is to continue to make prints while there is an issue with one or more of the colours missing, when the print head is used without all inks present then the nozzles overheat and burn out the electronics that control these colour nozzles..
When you need to do now to replace the current print head and then the printer will work ok for you..
O’ you said your new printer out of the box had a damaged print head, that’s not so, and if you still have the print head it will work if inserted into the printer again..
The Pro 1 has AI controlling its Epsom chip and sometimes it gets it wrong, powering the printer off for an hour, unplugged and then reinserting the power plug usually causes a reset and the printer will then work..
I hope this information is useful to you..