On my brand new MacBook Pro 13-inch I added a Thunderbolt 3 to USB-C adapter to connect it to my external monitor.
Any suggestions on how to make the external monitor see my laptop is appreciated.
A couple of things going on here. You probably used the official Apple miniDisplayport to DVI right? Apple never made a Thunderbolt to DVI cable so I'll assume thats the case.
You mention Thunderbolt but your old MacBook Air was actually acting as a DisplayPort over the Thunderbolt port. The USB-C port on your new Mac can do more or less the same. Thunderbolt doesn't enter the equation and the Thunderbolt 3 (USB-C) to Thunderbolt 2/1 adapter (with the miniDisplayport plug) won't work for this conversion; the TB3 adapter does not carry DisplayPort Signals. I wouldn't be shocked if Apple told you it would work; this happened to alot of people unfortunately.
You need something that can take Displayport over USB-C and convert to DVI, there are a few options on Amazon:
https://www.amazon.com/Cable-Matters-Adapter-Incompatible-Displays/dp/B012B58JRM/
Things change if you are trying to power something higher end like the 30" Apple display.
I can't make any recommendations because my old DVI monitors are boxed up, but there are plenty reviews.
