(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.
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!