According to Greater Anglia website, you can add day travelcard to your GA smartcard:
https://www.greateranglia.co.uk/tickets-fares/season-tickets/smartcard
What tickets can I get on my Smartcard?
Your Smartcard will let you load up to 5 Smart tickets at a time.
Travelling Monday to Friday – Season ticket (Weekly, Monthly, Custom Period and Annual) and Travelcard Season tickets.
Travelling every now and then – Flexi Season ticket
Travelling very little – Anytime Day tickets , Off-Peak Day tickets and Travelcards
I think it’s important to buy a ticket between Brentwood and Liverpool Street during the peak hours and select travelcard as your delivery option, but you’d need to be able to give your card number to receive the order.