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How high you should tee the golf ball up for your first shot on a par 3 hole really depends upon the club that you are using to play the shot with.
If you are using an iron or hybrid for the shot distance to the green, then you need to set the tee peg very low to the ground as you want to achieve a downward striking action with the club head through impact.
However, if you are using your driver or fairway woods for the required shot distance, you need to set the tee peg higher as these clubs are much more effective if you use a sweeping action and you strike the golf ball slightly on your up swing.
If you look at the depth of the club face on your woods, you will notice that there is a great difference between the depth of your driver face and that of your fairway woods. You want to work on setting the tee peg to a height level with about the second groove, or line, down from the top of the club face. This tee height should then allow you to set the golf ball at a height that results in the ball being higher than the club head by about half a golf ball. This will allow you to swing your golf club and with the correct ball position and swing, you will catch the ball on your up swing, striking from the centre of the golf club face, hitting a solid shot with the correct trajectory.
If you are playing your irons to achieve the required distance on the par 3 hole, then you want to set the tee peg much lower to the ground. Your irons are designed to make a downward striking action through impact. This means that you need to strike the golf ball and then the ground, so setting a lower tee peg position will promote this to happen. For iron shots set the tee peg just a few millimeters above the ground, as you would usually be hitting this club directly from the turf.
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If you set the tee peg height too high and the ball is completely above the top of the golf club head that you are using, then you will hit the golf ball too high and because of the high trajectory and angle that the golf ball is struck in, the shot will fall short of the target as it travels up too much and not forward enough.
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Teeing the ball up on a par 3 makes the shot a lot easier to play effectively well. Playing directly from the ground means you have to be more accurate with where the lowest point of your swing arc is, or the low point for the club head as it travels around you. If the low point is slightly before the golf ball, you will strike the ground and then the ball which will result in a shot that does not travel as far as it should. If the low point is too far beyond the golf ball then you will strike the top of the golf ball and this will produce a low shot that lands early and does not travel the required distance.
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Tee height is absolutely crucial if you want to hit an effective golf shot. To create consistency with your shots, use the correct tee height and always use that height with that club. If you use a tee that is too high, you may end up swinging the club head completely under the golf ball and not even striking it, just striking the tee peg from under it. If you tee the ball down too low, you will not strike the ball at the optimum launch angle to achieve height and distance.