This faucet is less than a month old, so this is not about any sort of build up in rust or minerals. I have used it less than ten minutes before it failed.
Here is what I tried so far:
Checked other faucets in the house, they are working just fine.
I disconnected the water sources and they are working just fine.
I took off the aerator and made sure there's no obstruction.
I'm attaching a picture of the only part (left) that I can't verify is the failure point or not. Not sure if it's some form of anti-flooding mechanism or not, but I can't disconnect it.