If you are going to buid a traditional foundation, you can do that with concrete. Many such structures have been built and have worked very well. However, the foundation must be built in the dry. This ussually done inside a sheet pile cofferdam. Often underwater (tremie)concrete is used to seal the dam, but it is not used as a structural element in the foundation. Although the concrete can be used as a bearing surface for the final structure. This type of construction can be quite expensive and thus the piles mentioned by Zambo are often a good option.