You need a sump. There is no other way. It can be as simple as a HOB
overflow going into a 5 gal
bucket. The bucket would need a small pump, like a MJ 600, to feed the skimmer and another pump to return the water back to the tank.
You would feed the skimmer from the MJ in the bucket and the skimmer would have to dump back into the bucket. Basically, a sump.
The reason you can't use a skimmer by itself under the tank is:
1- the pump pushes water/air into the skimmer
2- no way to "pump" the water up into the tank
3- the output must be below the neck of the skimmer. It's what determines the water depth inside the skimmer. If the output is higher (like going up into the tank) the water will just pour out the top of the skimmer until the water level in your tank drops below the level of the overflow and can't feed it anymore.