Came here to say about the same stuff that esshup already said.

After 4.5" of rain, even a leaky pond should be holding a little bit of water. Your observation suggests either there is very little surface water area (watershed) that runs into the pond, or the pond basin is almost 100% sand and water runs back out of that material almost immediately.

The solution to each problem is different. However, there is a chance you have both problems!

Even if you install a liner and create a perfect seal, you still need a water source. Either surface water or a well capable of a decent flow rate.

Good luck on your pond project!