(obligatory "I am not Chinese")

So the reason Google thinks that 世大 says "World University" is because it interprets 大 as an abbreviation of 大学 which means university (学 means study/school, so 大学 = big school). Abbreviating 大学 as just 大 is a common practice with university names, cf. "U" in English.

To figure out how to translate "big world" into Chinese, let's look at the right placard of Tiananmen.

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世界人民大团结万岁 — "long live the great unity of the peoples of the world"

This sentence breaks down like so

世界 - world

人民 - people

大团结 - great unity

万岁 - long live

So we see in 大团结 that 大 comes before rather than after 团结, so you were mistaken to think that 大 was a suffix.

And you might also notice that if you got rid of the 大 that every single word in that sentence is exactly two characters long: 世界・人民・团结・万岁. The reason for this has to do with how limited the syllables of Chinese are, so single-character words are actually fairly rare: 世 is read as shì in Standard Chinese, but there are dozens of other characters which are also read as shì, so in speech it becomes confusing to have too many single-character words like that. This is why the Chinese word for "world" is 世界 rather than just 世 or 界, even though both of those characters by themselves can already mean "world".

The magic word here is "morpheme" — ABChinese made a whole YouTube video series explaining the deals with single-character and two-character words in Chinese: part 1 ・ part 2 ・ part 3

In any case, if you take all of this together, you would understand that "big world" or "great world" would be 大世界 in Chinese — which, wouldn't you know, is actually the name of a famous amusement arcade in Shanghai, the Great World!

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师大 sounds similar and is a shorthand nickname for East China Normal University

I dunno that's what it made me think of. you could conceivably interpret 世大 as "world university"

EDIT: to be extra clear 大 is not a suffix, it is short for 大学 university (literally "big learn/study")

You're definitely off to a good start, and that's awesome! For cases where you're trying to learn though, I'd transition from Translate to using Pleco. I also though wasn't able to find something good on Pleco, if 世大 is a word it definitely isn't a common one. It honestly might be a name, idk the context you got it from.

I learned 世界 as world(as in 他是世界上最大的人 “he is the largest/biggest person in the world” or literally “he is world on most large person”) but I haven’t learned either character separately yet, so I can’t really help there. As someone else said, university is 大学. I also am hoping to get to where I can read 三体, I even bought the trilogy in Chinese while I was over there. I’m nowhere near ready though, even some social media comments are too much for me still.