I love Discourse Automation for stuff like this. I wasn’t able to send an email, per se, but I did send a custom message to a new user upon signup. I created an automation that sends a PM when a user joins a group, in this case trust_level_0.
Here is a screenshot of the compete automation:
Immediately upon creating a new account I had the PM waiting for me:
And the PM itself:
Wow, that is fun, I just want to play with all the automation! 
@Helga_Razinkova, if the available actions don’t work for your use case, you might be able to add your own action, and that documentation is available at: