How does the top secret security clearance process work for a specific MOS? Does it occur before or after basic combat training?

For an initial term Soldier joining basic, they screen your records and give you an interim. You can attend training with an interim but need an adjudicated clearance to maintain the MOS.
For a retraining like yourself, each MOS may be different. You can still attend training with an interim, but you might not be eligible for the interim. HQDA doesn't like to have holdovers sitting around at AIT for a year waiting on a clearance

SPC (Join to see) This is specific to my Air Guard unit, but we send kids to BMT after the background check process gets started. They then get to have that portion of training completed while the process is on-going. Unfortunately, there are so many going through Intel (& other AFSCs/MOSs that require TS clearance) that the process is still prolonged - DoD took back over all military checks earlier this year due to OPM having too many issues getting them all done promptly. This typically results in our kids waiting about a year between BMT & getting to go to Tech School. That, and the fact that getting a date for Intel school is proving to be very difficult right now due to the numbers of people that are joining that AFSC - so many that they currently have a day shift, and a night shift at Tech School.

As a rule after, and their are not many MOS's that require a Top Secret Clearance to attend advanced training. Secret, maybe but that can be handled with an Interim clearance.
Had to have a Confidential for Radar Maintenance back in the early 70's a s a private but unless you were working crypto or Nucs did not know people that needed a TS. That came much later as an Officer.

The clearance paperwork is processed while you're in basic. However, there are times when a delay happens. In some cases, those trainees were held over at the training company until either the clearance came through or it was denied and the soldier's MOS was changed. In almost 18 Cycles on the Trail, I had about 5 trainees who were hold overs waiting on clearances. Most of them came within a week and they shipped out, One ended up being reclassed after about 2 months and then departed to her training. During the time there were held over, we used them as drill corporals and helped us run the platoon. I've attached a picture of one of them I had. He's wearing a helmet liner with corporal strips pinned to it.

Depends on the type of clearance. I initially enlisted with the Navy (signed contract) and after Congress got me out of that situation, I joined the Army. My job required a secret security clearance but they didn’t even start it until I got to my unit after AIT.