I’ve tried multiple times to impede creek water. The last time I did it right. I cored it, used good clay, riprapped it with rocks of all sizes, built an overflow and concreted the whole thing. It also washed out and I gave up.

For a crossing, I think I would dig down, fill it with concrete, and somehow make sure that the water would have no way of pushing against it.

A load of five to eight inch rock is your cheapest and best bet.
You want to lay a solid bottom to the crossing that the water can wash over and not wash it away.
Most ranchers in the sandy soil of south Texas do this to their creek crossings, and with that said if it's a live creek that catches most of the runoff from the countryside, anything you put in the creek that isn't a slab or anchored will wash away.
Be warned, if you have cattle or hogs, they will either use it to water, or the hogs will make a wallow anywhere the water pools up.

I have a creek that runs across my place. I have done a couple of things and here are my results.

I have several natural springs on my place that keep water thru the year but the creek will dry up at both fence crossings.

First time - I have a pea gravel pit so I loaded numerous dump trailers full of pea gravel and dumped in the crossing. After each dump, I would spread out with a track skid steer and pack. This lasted about a year before ruts started forming again. The pea gravel just washes away during heavy rain flows.

Second time - I used broken concrete and bricks from a house that was moved. Took numerous loads with the dump trailer. I paid a dozer to clear out a fence line I was replacing so I had them pack the bricks in the 1 creek crossing and concrete in the other. The broken concrete did not do so well because the water washed all of the dirt around/under the concrete pieces and made it really rough. Every now and then I have to move the concrete pieces out of the way. It's been about 2 years. The bricks are still holding up good. Bad news is I'm out of bricks.

Best option so far - Bricks packed by a dozer
Worst Option - Pea Gravel

I came up with an idea after hearing about the semi trailer idea. I want to take a old cotton module trailer and cut the baskets off. Then place it across the crossing and pack dirt at both ends for ramps. You can buy these cheap. Ive seen them for free to couple hundred dollars. I actually have one on my place that I'm going to try out. Just haven't gotten to it yet.