The company 1SG will make the determination on who will be the PSG.
I have known many NCOs that held numerous key positions at the same time. An E7 is my last unit was both a PSG and a section NCOIC.
Those decisions were made through the 1SG and CSM. If he is competent and next in line, then most likely, he could end up filling that slot. You do not know but perhaps an E7 is inbound and will end up taking that position.
Back in the 90s, when I was an E4, the E6 Squad Leader got fired for incompetency and the next in line was this E5, who was also a major problem child. Our 1SG was an E7 and I was asked if I wanted to take over the squad. I said yes, and that was that. This was a Guard unit though but I have seen this happen in the Corps and there have been times in the active Army in which a junior Soldier has taken a leadership role over an NCO in a section. Not saying its right but if counselings justify it; then so be it. Rank does not guarantee a position whatsoever.
Watch the movie Southern Comfort and you see what I am talking about. It is about grunts.https://www.youtube.com/watch?v=R7V6gITreRA