Google - Google Pixel Manufacturing Defect

We bought a Google Pixel in March ****, and started using it fully in October ****. Around April ****, the phone started heating up abnormally and shutting down. This continued for a few time until it shut down and did not restart. We had to do a system reset (lose some important data) and it continued in the same cycle of shutting down. After getting it thoroughly checked by a google authorized service centre, we were told that the motherboard is faulty- and the cost of fixing this device would be more than half of its original cost.

To be noted that this defect in the motherboard is from the manufacturer's end- not from our usage. But since we are almost three months past the warranty, google is not willing to take practical responsibility for the discomfort and financial loss incurred due to their manufacturing defect.