how long until I can make E-4?

Entering as an E-3 doesn't give you any help at all when it comes to making E-4. You will just spend more time as an E-3. To be eligible for promotion to E-4 technically you have to have at least 6 months total time in service and 3 months time in grade as an E-3. But in order to get that you'd need a waiver.

Promotion waivers for E-2 thru E-4 are allotted by the Army to each company. Every month the battalion S-1 will send a list out to all the company commanders of everyone in their company eligible for automatic promotion, and those eligible for a waiver. BUT, each company only gets a certain number of waivers for E-2, E-3, and E-4. They're not just generic promotion waivers, they're E-2, 3 or 4 specific waivers. So all you'll be concerned with is the E-4 waivers. It's primarily based on how many of each grade they already have, how many total are in the company, etc. So a big headquarters company will get more waivers than a small line company. Some months they may get 0 waivers. They might usually only get 1 or 2 E-4 waivers per month. I've seen a company CO up at battalion hopping mad because he wanted to promote some guy in his company that he thought was a badass, but the kid needed a waiver and his company had none available. They had to tell him, sorry you'll just have to wait for another month. And quite often waivers go unused. Just because a CO has a promotion waiver available doesn't mean they have to use it.

There is no way you'd get a waiver at the minimum time. No CO would waste a waiver on you since by then he'd barely even know you (if he knew you at all) and since you're entering as an E-3 and have a long AIT, you'll still be in training. No training CO is going to give out a waiver. For what? In my experience most people who got waivers for E-3 and E-4 (I never saw anyone get E-2 early, which is automatic at 6 months) only ended up getting promoted 1 or 2 months before they would've automatically gotten it anyway. E-4 is automatic at 24 months, unless you have a promotion flag or really p*** off your CO. You can expect to be an E-3 for 24 months and to make it when everyone that went in with you as E-1's gets it also. At best, if you try to be Mr. Gung Ho, you might could hope to make E-4 in 20 or 22 months. What MOS you are is completely irrelevant in the promotion process until you are talking about making E-5. And your friend is wrong. It does not start after AIT. Your time in service/time in grade clock starts day 1 of basic training. Though I'm not sure how the waiver allocation process works for AIT companies, if they even bother trying to figure it out. The only exception to all that is 18X candidates. If you qualify to enlist for special forces, and get selected, you can make E-4 in 12 months while you're in SF school. And if you're a Ranger school graduate (despite the common misconception Ranger school is a small unit leadership school, it is not some sort of commando training) then all time in service and time in grade requirements are waived up to E-4. But nobody is going to Ranger school as an E-3 unless you're in the Ranger Regiment. Even then you'll probably be an E-4 before you go.

Oh, and promotions are always done on your anniversary date, to keep a well established seniority. If for example you enlisted today 9/15/2015 you'd be eligible for automatic promotion to E-4 on 9/15/2017. If you got a waiver and got it a month early your date of rank will be 8/15/2017, etc.

it starts when you start basic

its gonna take 24 months to make e-4 at a min

it could take longer

d