The shodanshok's comment is right:
If you can't telnet the SMTP server, the connection is blocked at the
gateway or server level.
So I opened a ticket for Digital Ocean's support and got the following response:
To curb a recent increase in abuse and SPAM, we have an initial SMTP
block on new accounts created in certain contexts.
To remove that block we'd like to do some manual account verification.
Please let us know the following:
- Your Name
- Location
- Phone Number
- The reason you are requesting the removal of the SMTP block
Also, please provide as many of the following as you can to help us
verify your identity:
- Your public Twitter handle
- Your blog
- Your company or personal website
- Your public Facebook profile
We take SPAM very seriously as we comply fully with the CAN-SPAM Act.
If you're not familiar, this says that you may not send bulk email
unless you maintain a double-authorized list of subscribed members
including IP addresses and relevant contact information. Also, you
must follow guidelines for including removal links with all sent
emails according to the CAN-SPAM Act.
I provided all the information and Digital Ocean has unblocked the SMTP connection.