In short, you cannot. As stated in this post
], a mechanism had been implemented in SMTP protocol for testing the existence of a specific mailbox, but the most use it has ever found was with malicious requests, not legitimate ones. So about every mail system is actually configured to lie when such a request comes in.
You still have the option to effectively send an email to said mailbox; if the server responds to you with a
5.5.0 Mailbox unavailable
code, then you know the mailbox does not exist.