Another objection will be familiar to students of Christian history. Taymiyyah contends that everything begotten is posterior in time to its begetter. Thus, if the Son is begotten, he must be posterior in time to the Father. But that would mean that the Son is not co-eternal with the Father. If he is not co-eternal, he could not be the same God, for the divine essence is eternal.
This objection was raised also by Arius in the 4th century. It does not avail.
The source of being need not be temporally anterior to what derives from it. Of course, in the world of animals, the parent always precedes the offspring. This is because we live in the world of matter, and matter takes time to be formed. You cannot be a parent on day 1. You must first come to maturity. Similarly, your offspring does not spring adult from the womb. (Thanks be to God.)
However, there are “sources” that are contemporary with their products. For example, in an argument, the premises are the “cause” of the conclusion. However, they are not necessarily temporally prior to the conclusion. Picture the sun and its rays. The sun is indeed the cause of its rays; however, these are practically contemporary with the sun. Of course, we now know that light does take time to travel. So that example is only an approximating example. Another would be gravitational attraction. If two bodies exist, they are necessarily gravitationally attracted to each other. Their attraction does not have a “time lag” but co-exists with them. Thus, being a principle of something is not necessarily to be prior to that something. There is no necessary proportion between causing and time. The only necessary relation is this: The cause cannot cause unless it exists.
Consider the divine, now. Many solid Muslim thinkers contended that Aristotle was correct: The world can go backward infinitely in time. (Aristotle thought it had to go back, for various reasons. These thinkers agreed that it could go backwards infinitely.) That is, the world could “always have been”. Yet, all these Muslims agreed that that world would depend on God for its existence. Thus, God would be a principle and yet what he produces would always obtain. I think there is nothing implausible in this. Aquinas argued the case compellingly in the middle ages.
The net result of all this: It is no objection to say that if the Son is begotten, he must be posterior to the Father. These need not be the case. Thus, the objection fails.