When someone is arrested, a bond may be set by the law enforcement officer. If so, the arrested person can post bail and be released immediately. If there is no bond initially, the individual will appear before a judge at a preliminary presentation hearing.
If someone accused of a crime does not have the option for a bond, the first court date is normally the arraignment court date. In a normal situation, you could expect your first court date to be about 3 or 4 weeks down the road after an arrest. Of course, some offenses take much longer to investigate, but they rarely take months or years to investigate before you receive a notice for your first court date.