Is there a way to tell where your divot would have been while hitting off a mat?

Either lay a few strips of wide blue painters tape down in the direction of your "target" line, or sprinkle some flour or talc powder on the mat.  Either method should let you see where the club is striking the mat.  If using the tape, you could make a small line then set the ball right on top of the line.  Should be very obvious where your club hits the tape from there.

2 things I do on mats with painters tape,

Option 1: place a strip directly behind the ball and practice hitting the ball without touching the tape but making sure you do hit the mat.

Option 2: place a piece of tape 3-4 inches in front of the ball and practice hitting the ball and scrapping the tape.

I find option 2 is the best when you aren't hitting it well because it gives you a good focal point however, once you get good at it switch to option 1 so you don't have to constantly replace the tape.

option 3: put both pieces of tape and practice missing the back piece and hitting the front piece. Bring lots of tape.lol.

While trying what the others suggested, pay attention to the feel and sound.  You'll learn tell the difference between crack-thud and thud-crack .

great idea!  THANKS

rock climbing chalk is cheap

flour is cheaper.

Range attendants much prefer tape...(assuming you pick it up and toss it when you leave)

If you're trying to cure yourself is hitting it fat, try putting a towel a couple inches behind the ball.  Move it progressively closer as you get more and more confident striking the ball.  Nothing cures hitting it fat like the shame of having to retrieve your towel repeatedly from down-range. Otherwise definitely painters tape, I'd hate to use a mat after someone covered it in chalk or flour or something.  I don't really want my clothes covered in it.