In Act 1, Scenes 1 and 2 present us with the anxiety brought about by Caesar’s return from war, killing the previous ruler, Pompey. The mood is frenetic. It is noisy. The people in the streets are shouting, and there are games going on because it is the Feast of Lupercal. We can imagine Caesar and his troops marching into the city, with all the flourish that involves. Some soldiers are grumbling, angry with Caesar. As a result of the festivities, perhaps, a soothsayer is wandering about as well, and he goes up to Caesar to give his prediction, which surely creates more anxiety and makes the mood ominous. Then we learn that the crowd, in their adoration, offers Caesar the crown three times, only for him to refuse it. To be sure, this happens off stage, but the excitement flows over into the speeches of Casca, Cassius, and Brutus afterwards. We also hear that Caesar had an epileptic attack, which must have put quite an edge to the voice of the speakers as well. The anxiety and "edginess" in these scenes lead nicely to the more dramatic scene of the storm in Scene 3.
You really need to look at scene three to get the true picture of act one. The first two scenes are excellent introduction scenes, but mood certainly isn't a focal point. As scene three opens, we have two conspirators out wandering through a storm riddled night contemplating the fate of Rome under Julius Caesar. The storm is a significant show of the ominous thoughts of the conspirators: bad things are afoot! We have a small feeling of uncertainty about whether or not they will be successful in recruiting Brutus to join the faction; however, by this time Cassius has been established a shrewd manipulator and we fully expect him to be successful in landing Brutus as an ally. By the end of act one, our mood is bordering suspense, but not quite there. The assassination of Caesar is still a distant thought because of the importance of gaining Brutus's support first.