You can drown In a cm of water.
No you can't. Water is dangerous but it's not a child's kryptonite.
Drowning is suffocation by water.
To drown, both nose and mouth need to be fully submerged, fully cutting off oxygen.
You need about least 2-4 fl.oz in your lungs to drown. To put that in perspective, go look at a Dr. Brown's 4oz bottle. That's a half to full bottle amount in your lungs needed to cut off air supply.
If you're facing down in a CM of water, you're inhaling air with the oxygen and it's unlikely you're breathing in at a force that's going to actually suck enough water in. For an infant you need about 5 cm (which is still less than 2 inches). Falling in a puddle is probably going to be fine.
It also means that if your child falls over into water and gasps in surprise under water, they'll die pretty quick if they don't get it out quick enough. Remember the bottle? That's about one full gasp. How long does it take to gasp like that? Probably shorter than it takes you to reach from a few inches away to scoop them up. From there it takes two minutes of no oxygen for permanent brain damage to occur.
So if you're pottering around the house letting your 19 month (Srsly KP86?!) play alone, you damn well better know rescue breathing and be prepared for a life of difficulties as they are no longer able to process things as sharply from brain damage. That's best case scenario. Worst case, you're frantically watching your child turn ice blue as he doesn't cough up the water like he should. That's not the last image you want to remember your child by.
Always, always be there with your child in the tub. But have a realistic understanding of what water can do.