Depending on how much mud you have before you get to firm clay, you might be able to put the posts on the bottom without doing any digging. I have built several piers in water up to 5 ft deep without setting the posts. I usually nail a 5 gallon bucket onto the bottom of the post and fill with rocks to help the post to stand up. The weight of the post, bucket of rocks, and framing lumber will cause the post to settle in the mud and the bucket will give you something to get a grip on to move the post around to get it set properly. That method has always worked well for me.