OK, I'm finished for the day. Feet up. Telly on. I've made my watch box; fixed a Rolex box; repaired a Seiko; been in to the shop; stripped and cleaned a host of little bits waiting to be silver plated .... So, let me impart a little Moka magic:
First, moka pots don't like fine grounds. You've said you don't have a grinder and so must be buying pre-ground. Don't buy anything that says "espresso" on it. Usually that means it's over-roasted but, at the least, it means it's finely ground. No good for a moka pot.
Instead, get a medium roast and medium ground coffee. Next, don't fill the pot with cold water; fill it with water just off the boil. Obviously, be careful. Fill it to just under the over-pressure valve. Put the coffee in the middle and screw the top on. Use a dry cloth to insulate.
Next, the pot goes on a low to medium heat with the top open. Watch the pot. As the coffee comes through, let it fill a third to half way, then remove the pot from heat and drop the lid. The pressure in the pot will be enough to finish the brew.
Try it that way and see what you think. If you want, I'll explain all the reasons this method works best.