You can make most showcase recommendations yourself through the showcase website. That is what we did. No one ever turned away our money. I think that is the most common way to get an invite.
Don't know the age of your player but - after our player finished his summer 16-yr old season we asked for a letter of recommendation from the coach. We used it in many mailings to colleges. I'm convinced it helped direct the path that led our son to his college team.