If a cruise leaves at 4pm. What's the earliest that they will let you get on?

 It depends on how quickly they get if off loaded and cleaned up. I have seen it as early as 10:30 am but wouldn't always count on that. Usually by noon you can board and be served lunch on deck.

On our 1st cruise we did go right to our stateroom as my husband and I were excited and wanted to see our stateroom and he wanted to wait for our luggage (that took awhile) so the 2nd time we took our time.   

We checked out of our hotel at noon, took a short taxi ride to the Port and boarded shortly after noon.  That gave us plenty of time to grab lunch and relax before we went to our stateroom which was probably ready.  This time we did not have to wait long to get luggage.   (We were really excited on our 2nd cruise too)  

I have only cruised one other time.  We waited to board around 2:30.  I must say, when we got aboard...EVERYONE seemed like they had been there a while...and had spent some time and money at the bar on the Lido deck.

We leave in 3 days.  We will probably try to board around 1 this time.