Sharp Consumer Electronics

Background:
I bought this Sharp microwave oven in July, the Amazon Prime day. I was heating some milk with a ceramic cup using the microwave oven. I saw some flashing in the oven and some fumes came out. I immediately unplugged the power and found a burn mark. UMC UK, the Sharp UK maintenance service, declined my warranty service request says that I misused the microwave. They said debris must had been on the waveguide cover so that it was burnt during the cooking. They also said it must had been a repeated misuse. However my oven was clear and had regularly been cleaned the internals. They drew this conclusion simply by looking at the picture without even checking the functionalities of the microwave oven.

Thoughts:
After 30 days the proofing burden is on the customers that the products which were faulty while we initially bought it. How much does it cost to compile an independent expert report claiming that the product was defective when bought and fight the legal proceedings?