Been there, done that. As you can see in the picture I've attached, I did something similar. In my case, I was filling in a hole from a tree stump that I had let fill with rain water. It was a spur of the moment idea to fill in the hole as I was driving the dozer back to the barn towards the end of the day. I saw that water in the hole and thought to fill it in and stop it from holding water. That was a big mistake.
The dirt turned to oatmeal in the hole with the water. The more dirt that I put into it, the better it looked, but then when I tried to drive over it, I sank. The first time, I got out, but I'm not so smart, so I did it again. That's when I sunk. Then I made it worse by trying to get out and digging myself down deeper.
It took a full day of digging with my backhoe and shovels to get it out. The tracks were just spinning and the weight of the dozer was on the belly pans. It acted just like a suction cup and nothing was going to happen until the tracks got down to solid material. I had to tunnel under the dozer and remove that mess in order to get the tracks to get down to the solid dirt that I had dug down to with the backhoe.
In your case, I don't think that pumping the water will work. I'm not even sure that the problem is water table related, but it could be. I think that you broke through the sand, which was more stable and able to support the weight of your tracks, and into the silt, which has no ability to support any weight.
I don't think you can dig down to something solid to get out, so that leave you with two options. Neither are good.
You can try to pull it out. With enough power, this will be the easy way to go. One advantage to a small dozer is it doesn't weigh very much. I got a JD 450G stuck in the mud once and was able to pull it out with my backhoe. Just hook the chain to the dozer and the hoe bucket and pull with the hydraulics. You will always have more power with the hydraulics then you ever will with tires and traction. If that's not an option, then a tow truck might be needed with a big winch. In the end, this might be the cheapest way to go. Just bight the bullet and write it off as a learning expense.
The other way, and the physically demanding way is to cut and place logs under the tracks. You need to create a mat. Imagine a log raft like Tom Sawyer would have used. Get some logs that are longer then the width of your tracks. You will probably need at least a dozen of them, but it might be more depending on how bad it is. The size should be big enough not to break under the weight of the dozer. I'd guess at least 6 inches, with bigger being better if you can handle them.
I did this one time and cut down the trees with my chainsaw fairly close to where I was stuck. It wasn't as bad as the picture, and I was out in just a few hours. I never took pictures of that one.
I couldn't get the logs under my rear tracks, but was able to lift the front end off the ground with my blade. I had to put some smaller logs under my blade to stop it from sinking it, but once the blade was solid, I was able to get the front tracks off the ground a few inches. With a shovel, I slid the logs in under the tracks. My first attempt failed because I tried it with just a few logs. They just sank into the mud. The next time, I put allot more logs in there. Maybe too many, who knows. But it worked. I was able to get up on the tracks and just drive on out of that wet spot.
The longer the longs, the more they will support. It's just as simple as making that raft or mat. If you are unsure of this, go to youtube and do a search for excavator and mats or stuck excavators. There is a guy that uses them all the time with his excavator while working in mud. He's amazing and if you find his videos, you'll see how crazy or good a guy can be with them and working in bottomless mud. If I find the links, I'll post them here.
Good luck,
Eddie
