One of the biggest problems new students of the game have in being able to draw the cue ball is that they are simply not hitting the cue ball low enough to generate the backspin required for the cue ball to change direction and come backwards from the object ball.
Hitting the cue ball low enough requires a very accurate tip placement onto the cue ball during the final stroke. Getting to this accurate position requires a good bridge hand that holds the cue at good level and a cue that is angled nicely down into the bottom of the ball.
Having a level stroke is not what you want on a draw shot. Of course you don’t want to shoot downward at too much of an angle, as that will limit follow through and forward cue power, but you do want to shoot down into and through the bottom of the ball.
So many of my students drop their grip hand too far before their cue tip strike the cue ball. This causes the tip to raise and not hit low enough and is difficult to see oneself doing. Even many instructors may miss this when watching a student.
I’ve trained myself to watch closely what a player is doing and catch what is going wrong.
If this is your problem, I suggest you think of the draw as more of a stabbing the cue into the table than as a normal stroke.
Even though I teach to drop the elbow on the stroke, this does not mean to drop the hand very much at all. The grip hand will swing down and when the cue is coming in at the ideal angle into the bottom of the cue ball, the stroke than goes forward like an ice pick going straight down into some ice. In this case the cue will be heading down into the table.