HUD requires the home to be closed within 45 days. If you are paying cash you can close much faster.
Are you closing with the HUD attorney? Fearnley, Calif, & Price? If so they should be able to clear title quickly because they already have all the information. Just get your agent to schedule the closing with them. Your agent will need to call the attorney to set the date. Otherwise they will wait the full 45 days.
If you are closing with another attorney this could cause it to take a little extra time.