from this approach says: Is it conceivable for something to come into being and persist, or not?

If they say no, that is untenable. If they say yes, we say:

If we suppose that something comes into being each day and persists, then an infinite number of existing things must have accumulated by now. Although the cycle itself has ended, it is not impossible for something to come into existence during it and then persist without ceasing to exist. On this supposition, the difficulty is established. It makes no difference whether what persists is a human soul, a jinn, a devil, an angel, or whatever other existent you wish. This consequence follows on every position they hold, if they affirm an infinite number of cycles.’

[Ibn Taymiyyah’s Commentary]

I say:

Abū Hāmid identified the correct method of establishing the Maker’s existence as reasoning from something’s coming into being to the existence of one who brings it into being. He said:

“We know necessarily that whatever comes into being does not bring itself into existence, and thus requires a Maker.”

This agrees with what the most accomplished rational thinkers have stated, in contrast to the position adopted by some of the Mu‘tazilah and those who agreed with them, such as al-Qādī Abū Bakr, Abū al-Ma‘ālī, and others, who regarded this premise as requiring inference.