Cold for a few minutes and then the compressor turns off?

Hello,

It sounds like you might have a faulty A/C pressure switch.
As the compressor is functional, because you get cold air for a little bit.
But if the pressure switch if bad they it will provide incorrect signal and the compressor will shut off.
The pressure switch if located on the front left corner of the engine compartment.

There is also a high pressure safety valve that goes on the side of the compressor, which can trigger this issue as well.

https://www.2carpros.com/articles/how-a-car-air-conditioner-works

I have attached diagrams for your reference.

Please let me know of any questions.

Thank you.