Is this a new account that was only created by email address or an old Telegram account?
I can only speak for my problem but in my case it was an already registered GMAIL address that I have used sucsessfull many times before.
After typing my address and hitting the button "Get started" the "Loading" message appears and then nothing anymore and I didn't received any Login Code by mail.
Anyway, a few minutes later it was working again like expected
