I think you'll miss many of the jokes.
There is a scene where Gump is in a hotel room in Washington and he calls Security for the hotel. Frank Wills picks up and Gump complains that guests in another room are using flashlights, keeping Gump up. The next scene is archive footage of President Nixon resigning his office.
To a non-American, the scene must seem pointless.
An American would (should) know the story. In real-life, security guard Frank Wills surprised a team of Cubans burglarizing the offices of the Democratic National Committee (located in the same hotel where Gump is shown to be staying). It turned out that the burglars were working for G. Gordon Liddy, general counsel to the Committee for the Re-Election of the President. Liddy's allies in the White House, including Chief of Staff H. R. Haldeman and presidential aide John Ehrlichman, tried to block the investigation into the burglary. Eventually, the burglars, Liddy, Haldeman, Ehrlichman, and others all went to prison. President Nixon had to resign to avoid impeachment and removal from office. He might very well have gone to prison too, had not his successor, Gerald Ford, pardoned him.
The joke is that this formative crisis in American history was kicked off, not by Mills's vigilance, but by Gump's insomnia.
The movie is full of figures in American history or their expies. I assume even a non-American would recognize Elvis (Gump give him his signature stance) and John Lennon (whom Gump inspires to write "Imagine"), but did you recognize Bear Bryant, Dick Cavett, and Abby Hoffman? Are cultural element Gump supposedly invents (like the Smiley Face, jogging, and the expression "Shit happens") familiar to you?
Probably, half the scenes in the movie are improved by a through understanding of American history and culture. On the other hand, the movie grossed $347,693,217 overseas, so I guess non-Americans can appreciate the rest.