Unfortunately, it's possible your email provider just has it blocked or filtered or there is some other problem with Square Enix successfully sending to it. It could also just be delayed because of the demand. Some people getting it instantly could be anecdotal.

The good news is that if it says it has already been submitted, then it is checking the information you provided against a list of people it is regarded to have applied and found it on the list.

In case they couldn't email you successfully, you could try making sure that future emails reach you successfully by adding the address to your address book. The address is included in the announcement at https://fanfest2.finalfantasyxiv.com...s/news-tickets

It does say this as well. I don't know if it means there is no confirmation email, but it at least means there won't be one to say you didn't win a ticket.
Note that players who are not selected will not be contacted.