The opening scene is very significant. It introduces immediately the idea that those in political power rise and fall through violence and war and that others then will take their place. This is the truth that drives the play. Caesar came to power by defeating Pompey and his sons, killing one of them. Brutus and Cassius come to power by killing Caesar. Antony and Octavius seize power by defeating Cassius and Brutus in war, forcing both of them to commit suicide.
Another idea emerges, also. The Roman people are characterized as being fickle and disloyal to their leaders. Unguided by independent thought or principle, they are swayed by emotion. They cheer for Caesar just as they had cheered for Pompey before him. After Caesar's brutal assassination, they immediately accept Brutus as their leader, threatening harm to anyone who might speak ill of him, and this occurs just before they then fall in love with Antony and run Brutus and Cassius out of Rome. So, it would be safe to say that the first scene does act as a keynote for the play to follow.