How can I suggest changes to daily SOP effectively and efficiently?

Take copious notes and at the end of cycle review attach you notes to the survey, or hand them to you favorite DI. What I would not do is start telling DIs and instructors how you can fix here problems. You are one of millions of trainees and TRADOC designs and redesigns program after program. They spend a great deal of time with assessessments, field studies and the psychology of leaning. I am not saying you should share your insights, I am saying it’s about timing. Even if the cadre read and agreed with you assessment they do not have control of the training schedule. So save it for the end. When you are at your unit making recommendations will be looked at in a different light. You will quickly get a feel for who and who not to share with. Tact!

Do as CSM Darieus ZaGara said. Also know that Many MOS producing schools are painful and could be very much improved, but that requires a lot of planning and testing. Those testing times can produce substandard Soldiers. The Army sticks with what works, occasionally changing a block of instruction here or there, but not an entire course. It's essentially a rite of passage.

As a recently retired 35T, i appreciate you becoming a critical thinker and wanting to improve or fix problems. That is commendable and will definitely help you throughout your career. I truly believe Tangos are a different breed of thinker.
I guess it would be pertinent to ask you, is your feedback about the course or about your day to day life in AIT?
On the both accounts, you need to be self aware. You have been in the Army for about 5 minutes. If there is something illegal, immoral or unethical happening, it is your duty to report it.
You can absolutely tactfully speak with your instructors or DS, but i need you to realize the depth of thought, effort, planning and scrutiny has gone into every bit of your curriculum. I have personally been a part of two Critical Task Site Selection Boards (CTSSB) for the 35T MOS, where the most experienced 35T's from around the force, from the SFC-CSM and CW2-CW5, discuss at great length and decide what is the most critical and valuable training that you junior Soldiers will need to equip the force. That experience is handed over to TRADOC and our instructor/writers to design the course curriculum for you.
If your suggestions about SOPs are about your AIT day to day life, know that in this arena as well, more often than not, every piece of it is tried and true, and part of your journey to becoming a Soldier.
And CSM Darieus ZaGara is absolutely correct.