The hearing in Spain is only one side of the problem. The criminal case that triggered it is already moving in the United States, and leaving that part alone until the extradition decision would waste time. For the American side, speak with an attorney who deals with extradition to the United States:
https://arkadybukhlawfirm.com/practice-areas/criminal-defense-extradition-to-the-united-states/ . A lawyer there may be able to find out what prosecutors plan to do should the transfer go ahead. That could affect how the defense approaches the proceedings in Spain.