To get a non-resident Illinois carry license you need to take 16 hours of training, you can get 8 hours of credit for NRA basic pistol or better, or for a DD214. If you have that you can take an 8 hour course. I don't know if anyone is doing courses outside Illinois.
Question are you from Hawaii? Residents of Hawaii are the only ones currently being allowed to apply, supposedly because they have similar mental health reporting laws. The cost is a whopping $300 and expect it to take about 60 days, maybe more to get it.
If you get the Illinois non-resident license to carry you'll be in a very select group.
Just noticed your location is Michigan, there is a bill in the legislature to allow residents from about 10 different states to apply. I don't know if Michigan was one of those states. I have my doubts that the bill will pass this year.
The license to carry class does need to be taken from a instructor certified by the Illinois State Police of which there are quite a few in Illinois. The NRA basic pistol, or better could be taken in your state from an NRA instructor, you'd need a certificate to get credit from an Illinois carry instructor.