what are the requirements for promotion from E-3 to 3-4?

Since you're coming in as an E-3, you should make E-4 in about six months to a year. I'm also a Combat Engineer. I never been to Sapper School, but it is a great school for Engineers to attend. Sapper is basically the Combat Engineer equivalent of Ranger to an Infantry soldier.

Good luck at OSUT. The time will fly by, trust me. The MP OSUT guys will be training nearby (unless they moved all of the units around, I went through in 2001). We always had a rivalry with those guys lol. Good times.

E-3 tp E-4 is a company level promotion....

Once you have completed your training ....are assigned to a unit.... have the proper time in service.... are recommended by your supervisors.... pass a company promotion board

.....you then can be promoted

When I was in the Combat Engineers they did not have the Sapper Program.... about time they rewarded these brave hard working troops.... they do everything an infantry man does and sometimes they do it first (65th Combat Engineers Cu Chi Vietnam)

You will not be promoted to E-4 after basic, there is nothing you can do that will make that happen.

It will be a year before you make E-4, even if promoted ahead of time.