US military does not have the heavy lift (1,000 ton and more) floating cranes needed. Only some salvage companies have the needed cranes; they are likely working jobs somewhere in the world, not in the US & would have to make a sea voyage to begin.
It will be interesting to see what they do in the short term. My uneducated guess is that they cut in to smaller pieces that can be partially floated and drag the pieces of the bridge away from the channel.
This advice is free by the way. Worth much more for sure.
Military can provide manpower.
In the meantime, 1000 American soldiers are building a port to supply the damn Muslims in Gaza.