Does anyone have any solutions on how the contractor should fix this?

Your contractor should be solving this problem, not you.

You want them to own the problem and be responsible for the fix.

These "new" sliding doors always leak some water when taking a shower. They look cool, but the design just isn't water tight. At least you have a bit of a threshold so you don't get water just flowing out the bottom.

Get used to putting a towel down to catch the water.

I'd pay attention to how the shower is pointing while showering, particularly the handheld part. Can you change the angle of the shower slightly to minimize the problem?

Maybe reset the cap to pitch water back to the pan and cut some slots across the black track to allow water to evacuate.

Add a shower door sweep to the bottom of the doors. Or better yet, have the installer back to add the sweeps and check their effectiveness and also diagnosis the overall issue.

The problem is that the dam (the black metal piece) is inside the sliding door. It should have been outside the sliding door. With its current placement, any water that falls between the dam and the door -- and there may be a lot of it -- will seep under the door and into the hallway.

The doors should have been reversed with the sliding door inside the fixed glass. Then the dam would have been placed outside the sliding door and prevented water from exiting the shower into the hallway.

A shower door bottom seal (example) could be attached to the bottom of the sliding door to prevent water from leaking underneath it. However, the sliding door guide must be wide enough to allow the door and bottom seal to fit (slide) inside. The seal linked above requires a guide with a channel at least 1/2" wide. If your guide were too narrow, it would have to be replaced.

A sort-of solution: Move the dam as close to the sliding door to reduce the amount of water that can fall between the dam and the door.

Ramona and wdccruise nailed it. The sliding panel should be on the inside and the dam outside of it, so water sheeting down the glass lands back in the pan instead of on your floor. I would have the installer back to reset the door properly and add a bottom sweep with a drip edge, and double check the curb cap slopes inward toward the pan. This is not a towel situation on a brand new remodel. Water sitting on that floor will work its way into the grout and subfloor over time.

One check worth doing before the door is adjusted is whether water is pooling at the threshold because the pan is draining slowly. With the door closed, run the shower briefly and watch the water: if it starts to pond near the drain or around the threshold before it reaches the door, a slow drain or debris in the drain can make even a corrected door look leaky. Clearing that first, and having the installer show that water clears the pan promptly, gives a fair test of any sweep or door adjustment.

Meow: "One check worth doing before the door is adjusted is whether water is pooling at the threshold because the pan is draining slowly."

As shown in the photos, the pan is quite deep. The cause of the problem -- the dam is inside the sliding door -- was described earlier.

I agree with ramona1976 and wdccruise — this isn't a "put a towel down" problem, it's an installation problem. The sliding panel should be on the inside and the dam outside it, so water that runs down the door ends up back in the pan instead of on your floor.

I'd have the installer come back and own the fix, rather than accepting just a bottom sweep as the solution. A sweep can help, but it won't fix the panel and dam being reversed. Before they do the work, it's also worth doing Meow's check for pooling or a slow drain, so you can tell whether the pan is draining properly once the door is corrected. Take a quick video of the leak while it's happening — that makes it much harder for anyone to dismiss as normal splash.