You do not need to be baptised to be married in a C of E Church and most of the C of E (Aided) oversubscription criteria I have seen are about attendance at church not baptism. If you are planning to have your child baptised in the C of E the parents and godparents make these promises:
Minister: Parents and Godparents, the Church receives these children with joy. Today we are trusting God for their growth in faith. Will you pray for them, draw them by your example into the community of faith and walk with them in the way of Christ?
Parents and God parents : With the help of God, we will.
Minister: In baptism these children begin their journey in faith. You speak for them today. Will you care for them, and help them to take their place within the life and worship of Christ's Church?
Parents and God parents: With the help of God, we will.
Later on in the service there is a section called 'the decision' and there are various words that can be used but at the heart is the question:
Minister: Do you turn to Christ?
Parents and Godparents: I turn to Christ.
Another part of the service is the profession of faith. There are several authorised versions but this is the most commonly used:
Minister: Let us affirm, together with these who are being baptized,
our common faith in Jesus Christ.
Do you believe and trust in God the Father, source of all being and life,
the one for whom we exist?
Response: I believe and trust in him.
Minister Do you believe and trust in God the Son, who took our human nature, died for us and rose again?
Response: I believe and trust in him.
Minister: Do you believe and trust in God the Holy Spirit, who gives life to the people of God and makes Christ known in the world?
Response: I believe and trust in him.
If parent(s) want to explore Christianity then I'm happy to baptise but some of my fellow priests and ministers in the C of E will insist on attendance on an alpha course or similar first.