Can the Marine Corps help me get a job in Law Enforcement?

Absolutely not

Other than you will be in good enough shape and yu can account for your time

LAPD was, in the past, the only department that actually recruited, specifically form marines because of nearby bases.

Out of those 3 currently only LAPD is having trouble finding qualified candidates.

Being a marine or in any other service does nothing. Except all honarable discharge vets get a few points on entrance tests. Same for CPS and NYPD and all police in most states.but they have

Being a veteran can help you get law enforcement officer jobs. Veterans get extra points on civil service tests and preference for federal jobs. Some law enforcement agencies that require applicants to have college will waive some or all of their college requirements for veterans. Also, for different reasons, some people simply like to hire qualified veterans whenever they get the chance to. Some law enforcement agencies even give veterans a higher starting pay. Best of luck!

Well yes it can. Your infantry training will not transfer over to you police training. It will make it easier for you to get a slot.

It seems like you are not in the military yet. I suggest going MP (military police). If you can, go Army because you can sign for your job and won't have to hope you get what you want. It might also be easier to go reserve or national guard and then apply after you graduate your military training. It won't really make a difference as to what branch of service you join or your component (active, reserve, etc.)

It can help you when you get out with your GI bill to get the training you will need.