We had a similar problem in the university. At the beginning of the semester, the students have to register for a Moodle server with additional material. So when they create an account, we have to send a few thousands of confirmation emails in a short period out of the blue, that makes Gmail/Yahoo/Outlook/Whatever unhappy.
The solution was to ask the students to send an email to the server half an hour before registering. It's not ideal, but it adds us to a secret list of known contacts of the student, so (most) emails are delivered.
What are you confirming, and why do you have to send it as E-mail? If it's sign-ups, just "confirm" using the same system that the user used to sign-up. Presumably HTTP.
Frankly, I'm getting tired of having to constantly "verify" this and "confirm" that every time I sign up for or log into an online service. It's especially annoying after I've already signed up. Every bank that I haven't logged into for the last 5 milliseconds hits me with a "confirm your E-mail yet again" flow. I'm going to just start using "password" for my password if these guys keep insisting on round-tripping through my E-mail every time I need to do anything.
Also, an important use is password and username recovery. We even got password or username request 30 minutes after signup! They had quiz to solve if they want to help during studding and it's good to track them.
We had a lot of wrong emails, in particular it was common someone@yahoo.com instead of someone@yahoo.com.ar because Yahoo! offer both options. Also someone@gmail.com.ar that does not exist, but that never stop users.
(If it help, we never asked to confirm the email again after the registration.)
I'm in the first year of the University of Buenos Aires. Everyone with a high school title can get into the First Year, no filtration before the first year. There are more than 50.000 students per year. The fist years is shared between the 13 Faculty (branches?). Each one has a different policy about the email for students. Moreover, inside each faculty each department has a different policy about the email for students (IIRC ~20 years ago in computer science every student got an email, but in math you got an email only after getting a undergraduate-TA position in ~3rd year).
Now the whole University has a deal with Microsoft so I got an email there. And also the First Year has a deal with Google so I got another email. Each faculty may self host or has another(s) deals with someone else, so I have another email in my old faculty. Three in total. I may even ask nicely to get a email as visitor in other departments/faculties, but I'm too lazy to do that. And some coworkers work in two or more faculties so add a few more emails for them.
Back to students, I have no idea how many emails they get now. Also, they may get the email a few months after the semester began, or not, I'm not sure and in the best case we definitively can wait until all the paperwork is done.