Can I switch job within the introductory period after I sign the Non-Competition agreement?

What does your contract say?  Does it provide that the non-compete provision takes effect upon hiring or upon completion of the introductory period?  I would be surprised if it didn't take effect immediately.  However, non-compete agreements are scrutinized very closely by Courts and often held to be unenforceable, in whole or in part.  Numerous factors go into this decision - the industry involved, the position the employee had, whether and to what extent the employer spent any time or money training the employee, whether the employee had access to any trade secrets, how long the restriction if for, how broad it is geographically, whether the employee received any additional consideration (beyond getting or keeping the job) in exchange for signing the non-compete, etc. - so there is no bright line test to tell you if yours will be enforced or not. In most jobs, you probably would not face any legal consequences for quitting in advance of when your contract allows (although many employment contracts do not have a specific term; they provide for wages, etc., but are terminable at any time by either party), but this is not true in all cases.  For example, if you recall several years ago Kim Basinger was successfully sued for breaching her contract to star in a movie.  Likewise, while the fact that you were employed for only a short time before leaving for a competitor would cut in your favor when a Court was deciding whether the non-compete provision in your contract was enforceable, it is certainly not the only factor, and there is no guarantee that it will not be enforced if you are sued for its breach.