As other comments said, this happens by default

Yes, it would be good to email out using the alias without having received any email to the alias yet. E. g. for resolving problems or inquiry about status of procedure.

If it is important for Proton to block misuse of the alias function by using it as a second email address in the free plan, there could be an alternative form of limitational fencing:
Aliases could stay valid for a maximum of 6 months and be available for simple email reception and sending (including attachments). Expiration date should be displayed for each alias. I suppose most use cases regarding contact with potentially spamming companies would be covered inspite of such a limitation. And it could not serv as an additional email identity!

Just tested it. Works fine.
PLEASE close this issues as resolved / implemented!

Have the ability to send an email from a hide-my-email alias, I know you can reply using the alias but would like the ability to select it from a drop down menu (from the from section).

Apple is offering this for "Hide my Email" in Apple Mail, where you can select it as option from the "From" dropdown. It is a really great functionality, cause sometimes it is just necessary you contact services you registered for with an alias over an different mail like support@service.com, if you ran into problems with the service, and there you also don't want to show them your main Mail Adress

From the comments here it appears the feature already exists. However, when sending mails, it's very unclear if it is. Best would be to be able to select one of your aliases to reply with.

Additionally, the same would be useful for having a reply with your catch-all email. Example:
You can give theail address random-site@yourdomain.com on the fly. When catch-all is enabled and this email does not exist, it should automatically create this as a alias email (as you are the owner of the domain and it is set in proton, this shouldn't be that difficult as you can already do this manually anyways). So that when replying you can easily reply in the name of that email without sending mails from catchall@yourdomain.com

This feature is available. All you have to do is just normally reply from your email & it will automatically use your alias, even tho it says that it's using your email. That's something that could be improved because it's not clear enough.

If this feature is already available, will someone please tell me where or how to use it? What I see is that if someone sends me an E-mail using one of my aliases, if I hit the reply button, my account E-mail is in the 'From' field.

Giving out an alias is pretty useless if my actual account E-mail is exposed the first time I reply to an E-mail.

This feature is already available within the Proton offering.

You might need to create a reverse alias for the given alias first (I don't know if the are generated automatic) but if you reply, you reply to that reverse alias and hide your real mail address. You will notice if you look closely to the to: address.

So you might want to close this idea :)

Send mail from a hide my email alias

As far as I know, when you answer to the reverse alias with your proton email address, to the recipient appears your hide-my-email address. You can test it sending you an email to another email account (Gmail, outlook...).

There is no point in having alias email addresses if you are going to respond and forward emails using your proton email address.

There should be a link to you proton pass record to see if there is a matching email address.