Carpet install sequence

The carpet and firewall insulation were long gone by the time we got our 67 Barracuda ‘Vert.

We are at the point that I could install the firewall insulation, heater boxes, etc. and I got to wondering - should the carpet go in first? Does it matter?

Trying to get this project to the point I can take it to the upholsterer so he can install the top.

Thanks for the help.