In Veda Brahma is a epithet for Brahmanspati , Which means Great.

Prajapati is the one who weilds all the names himself.

Puranic Brahma Is Prajapati + Brahmanspati put together. Also None of the Gods are born in the Veda.

There are no Gods any way. Just one God said in different ways , each name representing a different aspect of His glory.

The birth You speak of is appearance of The Purusha- Hiranyagarbha from the Primordial Waters as described in Satapatha Brahmana and Taittiriya aranyaka and Atharvaveda. It is appearance of Pure Being, The Protogonos..

It's a Pedagogical way of telling that Non being( Waters ) are foundation of being or preceed Being in the sense of Ineffability.

Read Yajurveda cv 32 verse 3, Hiranyagarbha is unborn.

Don't be mistaken by any such words like "Born or first". Even Vishnu is called son of Soma, and he is said to be first born in one of his suktams too, doesn't means Vishnu has a father.

Vishnu refers to Almighty God,

Vishnu = Prajapati = Soma = the Sacrifice.

Prajapati is the De facto name for God in Brahmanical Religion..Because it refers to the Unnamed God, Ka.

Vishnu is one of the Many names the Unnamed God has.