Twilio evangelist here.
Not sure what you mean by "from the list of available phone numbers". Do you mean you've purchased a number from Twilio? If thats the case you do not have to verify it, you can use any Twilio number as an outgoing caller ID.
If its not a Twilio number, today the only way to authorize an outgoing phone number is to have Twilio call that number and for someone to answer and enter the correct pin code. The reason is to prevent fraud.
Hope that helps.