The only thing stopping me from getting this done is the verification email being sent, and it’s very irritating.
Welcome to the community, Ibraheem!
If you’re trying to send form your domain-based email address using your AWeber account, then the verification email needs to be sent to that email address, since this verification process is in place to verify that your inbox is working for the email address that you plan to send from.
This verification email will come from help@aweber.com, so it can be helpful to safelist help@aweber.com within your mailbox to help with email filtration. The verification email can be re-sent from the domains and addresses page in your account by mousing over the email address and clicking on the resend icon:
If you still experience trouble finding this verification email, then it would be best to reach out to your mailbox provider in case the email is being rejected on their end for any reason.