An interesting problem.

In normal situations your best shot is to put off crossing and continue on until you come across a bridge, viable ford or a boat. In the highly unlikely situation where survival on this bank is essentially zero and for some reason there is no time to explore to find a more favorable crossing site (zombies and/or velociraptors?) there are ways to slant the odds more in your favor and improving upon the low odds 'jump in and swim like hell' strategy.

First thought would be to make a boat, actually more of a float. The classic field expedient float is an option that allows exploitation of a lot of materials common to a lot of locations. The basics of building the float come down to using any water resistant sheet goods wrapped around materials that float or that can maintain an air space.

In one version you use branches, vines, sticks, to form a 'doughnut', more of a large wreath. Your gear gets stuffed into the center. Then the assembly is wrapped in sheet goods you have at hand. Ponchos and tarps are good but a tent, ground cloth, rain-wear can also be used. If you have two tarps/ponchos use the best one for the bottom and lash over the top. Use the second over the top to help keep air in and splashed water out.

If you have sufficient volume with pack/s or floats you have or create the doughnut frame of light brush can be eliminated. You are going to have to be creative. Stuff sacks can be filled with grass, leaves or sticks to create a float. Same with the legs of a rain-suit. Canteens, water bags and other containers can be emptied Make sure you still have some water if the river water in undrinkable.

The idea is not to produce an actual boat but to manufacture a float that will be buoyant enough to keep most of your body out of the water for the duration of the crossing and stable enough that you can concentrate of paddling and avoiding any large debris coming at you instead of balancing.

The second technique that comes to mind is to 'dress for success' A cold-water rated dry suit with gloves, booties, mask, and fins would be ideal. A thick wet suit a second choice. And I'm quite sure everyone reading this carries one, and a spare, in their hip pocket at all times.

Two different thoughts come up. First is the 'go naked and fast' method. If you can get across fast this is an option. The idea is that whatever you wear is going to get heavy, wet, lose the ability to act as insulation if worn. If you go nude the clothing might be kept dry and you can bundle up once across.

The other way would be to try to create a field expedient dry or wet suit. Wool and fleece drain well and once drained they retain a fair amount of insulation value. A rain-suit might be tightened up to keep most of the water out temporarily and insulation underneath might stay dry. The down side here is air trapped in your pants might keep your head under water and any water that gets in will weigh you down which could make getting out of the water slower and more difficult. Time in the river has to be minimized.

Okay, you have your float and you are dressed for the dance. How are you going to get you and the float across the river? Two things that come to mind are paddling and using the differences in water flow around a bend and pendulum effect to propel you across. A paddle might be improvised with a flat piece of wood or a piece of sturdy cloth lashed to a forked piece of wood.

The pendulum effect uses a long piece of line tied upstream to the side you are on and the natural tendency of the raft, held against the flow to move toward the faster moving water, to get you across on a bend. This method is used by some commercial ferrymen in remote areas. They use the pendulum effect to go one way and winch back the line to go the other. I'd make sure there was a fast way of disconnecting the line if the pendulum gets you most of the way there and you need to paddle the last bit or if you are being overtaken by a large object caught in the flow.

I would also think about having some light gloves and shoes to prevent damage on rocks and debris when landing and fending off. Something that leaves my regular boots dry and something that won't fill with water and drag me down. Swim booties, and light but tough synthetic work gloves would be ideal but other gloves and tennis or camp shoes would work.

Assuming you make it across it would be a shame to expire having overcome such a major obstacle so some thought should be made to warming up once you are across. Keeping warm clothing and a sleeping bag dry would be a good first start. One of the advantages of going bare is you start drip-drying as soon as you get out of the water and you can essentially dive right into a sleeping bag.

Having a stove ready to go, materials for a fire handy, a tent ready might also help. A self-erecting tent might be ideal as it would keep the wind off as you break out the sleeping bag.

Hint: Like most advance techniques prior practice greatly improves performance, speed of construction and execution, and outcomes.