Consider things like SOAR - that was explicitly an architecture for general intelligence. Whether it was any good or not is another question - but there was an active good-old-fashioned AGI field back then.
Mind you - one of the reasons I left AI research to do web stuff from '92/'93 onwards was I was pretty sure the symbolic approaches in favour back then wouldn't scale up and that there really was only intelligence on one side of a computer screen.
I dispute that this is because they don't poses intelligence. Whenever we find an animal displaying some ability we had said required intelligence — language, tool use, self-awareness, solving abstract puzzles, driving a car — we seem to change our definition of intelligence. Just like we have done with A.I., although probably because we want to eat the former and make slave labour of the latter. ;)
(Am vegetarian, please don't eat me, oh robot overlords!)
1934 was a turning point in this respect, by the 1940's it wasn't a question any more of whether or not atom bombs could be created, it was more a question of 'how' than 'if'.
Whether or not it's likely we'll see AGI any time soon is, IMO, a matter of wild-ass-guessing more than anything else. There are no experts in AGI right now, only philosophers, because the field doesn't even exist. So nobody has any remotely educated guess about what algorithmic discoveries need to happen and whether they're in reach for human understanding, or when we'd have the computational power to exploit such algorithms if discovered.
All we can really say is that it's theoretically possible, we're living proof of that. Also that there must be a lot of intelligent needles in the algorithmic haystack if evolution was able to stumble across one without a clear fitness mandate to do so (most of the creatures that thrive don't have what we consider intelligence, so it's not that evolutionarily important). I'd probably bet on it being more a matter of "when?" than "if?", but I wouldn't make any assumptions about timescale other than "not this year, probably not next".