Wow, as a former TL let me tell you the first mistake you just made that most TLs find out the hard way.
Do not coach TMs right after you promote!!!!!!!!!!! You sound almost like you are eager to do so, and haven't been able to yet because of training.
I can tell you right now if you go in during your first few weeks and start coaching you are going to have most of your team turn on you. They may not do it to your face, but behind your back they will have lost all respect for you pretty much from day one. This means you will be dealing with angry TMs who do sh** to make your life hard, be it intentionally not asking for red cards when you are gone or anything else they can get away with. (and FYI as a former TL - don't think they will only be hurting themselves, because the ETLs will be coming for your ass first before they do any TMs)
If you absolutely "need" to coach anyone, you get another GSTL to do it or if you are a low volume store you partner with the ETL-GE while you do it. Because these are established leaders that are doing the coaching TMs see it as being legit. New guy that just walked in the door and hasn't even proven himself as a leader in the building yet coaching people as his first order of business? You are going to get a lot of hate and disrespect. Nothing is worse than being a TL that every TM talks trash about behind your back, and that is exactly what it looks like you are asking for.... Don't think it matters? Just wait until the front end goes to hell on your watch because your team has lost respect for you from day one and your job is suddenly on the line with the ETLs.... At that point, it is not an easy situation to fix. You can lose respect a lot faster than you can earn it. Remember that.