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.

If it was me..

I would put in the firewall insulation, then the heater box. steering column seal, windshield wiper pivot seals, check cowel fresh air openings for rust holes and repair. Also, a good time to check/replace the heater core.
Then, I would test install and fit the carpet making sure to cut out the shifter and bracket locations for the console , the dimmer switch grommet location and lastly, the holes for the seatbelt bolts.
After doing this, take the carpet back out and send the car to the top installer with the drivers seat only. I'd have only the bare minimum interior in it as He's going to be crawling all over the interior when installing the top and **** happens like seats getting torn, door panels scratched etc.. After the car comes back, then install the carpet and the rest of the interior. I've been down this road getting a headliner installed . I learned this the first time I did it.