If you call GPRS 2G, then Edge is 2.5G, then 3G is 3G obviously. Then no data network at all would be 1G, which is purely voice and text.
GSM itself is inherently a 2G technology at a minimum.
1G wireless technology is analog (rather than digital) service -- mostly AMPS in North America -- and it was voice only, no text messaging.
The immediate successor to AMPS, D-AMPS (also colloquially known as TDMA, although several other technologies such as 2G GSM were also inherently TDMA), was used for a while in the USA before carriers moved on to either GSM or CDMA-based services. D-AMPS was a digital service that provided features such as text messaging, and it is also technically considered to be a form of 2G network.
AMPS has been switched off for several years now (so has D-AMPS), so no phone currently active anywhere in North America would ever be able to legitimately report being on a 1G service.