We’re already at a point where some people will start staunchly attributing AGI to extant technology and others will disagree, and the tides will shift in favor of the former as technology further develops and the (themselves very modern) traditionalists tire of fighting about it.
You’re thinking about the question scientifically, but neither language or culture work that way.
There is very likely to be a broad but loudly disputed consensus that “AGI has arrived” within the next few decades, regardless of what more the technology can actually do.
Academics will be writing about it as such, corporations will be asserting as such, legislatures will be codifying it as such, budding pseudo-religious movements will be vaunting it as such, and the many old cynics like you and me will just be saying “WTF?!” before resigning ourselves to watching Seinfeld reruns and feeding birds in our own private peace.
[1] Danziger, K. (1997). Naming the mind: How psychology found its language.
Serious question. I think we've invented AGI, but that term is now useless and we need to come up with better terms such as superintelligence, or maybe a numeric scale.
Without a definition, you can't say if we're remotely close.