Need help with thermostat wiring

Hey everyone,

I installed a google nest about a month ago. It’s been working fine for heating, but with today being a little warmer I decided to test the A/C.

When set to cool, the A/C condenser works for a split second and then stops. The nest then tries again 2 minutes later and the same thing repeats.

I’m starting to think my wiring might be wrong. When I put the nest in I didn’t grab a picture of the existing wiring, but most of the wires were labelled. What wasn’t labelled was an orange wire which I figured had to be ‘C’. Today I opened the panel on my furnace and the orange wire is actually connected to R, and there doesn’t seem to be a C going from my furnace to my thermostat. Just a C from my AC to my furnace. Looking at the wiring diagram, it seems like the orange wire currently connected to the R terminal of my furnace should be moved to the C terminal. This seems like a bold move to make without being certain, so any advise would be appreciated