I have long argued that one of the key proof texts for Calvinists who believe that God is sovereign in meticulously planning every event, Romans 9, is a misunderstanding of that passage based on failing to fully appreciate the context. And one of the key proof texts for divine determinism actually proves the opposite point when connected to its Old Testament roots.
The primary question of the book of Romans, particularly chapters 9-11, is whether God is breaking a promise to Israel in granting grace to the Gentiles. Why should anyone object to grace? He states it is "not a matter of man's willing or running" - it is not of the law.
In this context of mercy Paul does mention Pharaoh and a "hardening" of his heart. Specifically in vs 18, Paul notes "He has mercy on whom He desires, and He hardens whom He desires" (NASB)
Context matters. The idea of "Hardening" should be considered in light of Romans 1, where in reference to the entire race, Paul says God "gave them over" to depraved mind, a consequence of not acknowledging God. It should also take into account Romans 11 where the blindness of the Jews serves a purpose in reaching the gentiles but the state of national Israel's unbelief is not irreversible.
But the key passage is next in v19-25: