hi, i'm a formerly protestant coptic orthodox Christian.
sponsors are actually not common in coptic churches and other OO churches that i have asked about.
we do not have a part in the service for 'God parents' but we do have an arabic word for it, so it is possible to have them.
what i mean is that if a child is baptised, the parents automatically have the role of 'God parents' in the EO churches.
there is no formal arrangement about who takes the child if both parents die. family members / friends automatically step in if this happens.
if an adult / older child is baptised / chrismated, the person speaks for himself / herself and there does not need to be a God parent or sponsor.
however, it is common for new people coming into the church to be instructed in the faith by the priest and by other church members, and a relationship similar to the 'God parent' relationship may develop spontaneously.
i think this is because 'God parents' became common fairly late (after 300s) in church history, but i am not sure about this. maybe someone who knows more about this can comment.
in my own case, when my husband and i first visited the priest and his wife, we asked them 'what shall we call you?'.
they replied, 'call us mum and dad' and so, later when i joined the orthodox church, i told them i considered them my God parents.
they are very happy about this!
PS i forgot to say, may God bless your journey and guide you as you learn more of the depth of His love.