Nope, there are no "Beginning Earth, Water, Fire, etc." We have a mukyū (before they reach any rank) and then 9th-1st kyū.
This was written by John Lindsey on E-Budo about several elements and one of the three Gyokko-ryū bowing methods which correlate to the three first levels: jōryaku no maki = tenryaku uchū gasshōrei (天略宇宙合掌礼) chūryaku no maki = fūten goshin gasshōrei (風天護身合掌礼) geryaku no maki = hannō bonitsu gasshōrei (反応汎溢合掌礼) The last one, hannō bonitsu, is the one he is referring to. "Once when I was training with Tanemura Sensei in Japan I asked about one of the kamae from a Gyokko ryu kata and why we were using a specific hand seal. He told me: “your thumb is forming a ring with your water finger. The attacker is fire, and you are becoming water to counter him.” Since Tanemura S. was Hayes’ original teacher, I wonder…"
BTW, here is an article by Stephen Hayes called "History of the Go-dai No Kata" http://www.bujinkandojofinland.fi/uraomote/96march.htm#hist Looks like he made it up himself to me.
The five elements thing is really just a mnemonic learning device, nothing more. Similar to how Musashi's Book of Five Rings is structured. Some people just read too much into it.
I don't believe he was training before then, so I must of been mistaken. When I get back from Japan, I'll see if I can get my hands on it again from him and take a closer look. To the credit of the Genbukan, he moves incredibly well and has great technique.