I think part of the problem is that some (not all) Arms have a notion of prevenient grace that is chronological rather than ontological. For which there does seem to be some Biblical warrant!–but also for the ontological priority of prevenient grace. So it’s another both/and scriptural testimony.
In the ontological sense, prevenient grace is why we are rational souls at all who can choose one thing and not another (and so who can also repent). This, by the way, is why some Calvs consider the non-elect as not being persons at all but only as zombies (in the philosophical sense–I’m just about sure a Calv philosopher was who came up with that idea for philosophy, too, btw… ) In that sense, those Calvs are in fact just as much Christian universalists as we are!–God will persist to success in saving all sinners who by God’s grace are actually persons. It’s the same thing in principle as those universalists who don’t believe in the real existence of rebel angels; those sorts of Calvs just scope it out wider to include many apparent humans as non-persons who, by God’s choice, will never be persons. (Other Calvs, along with all Arms I suppose, and Kaths such as myself, would say this makes a hash out of many scriptural testimonies about God punishing people post-mortem as if they actually personally deserved it.)
Chronologically? I suppose there’s a sense in which that happens, but it’s not long before or after birth!–we’re talking about when a person becomes a spiritual soul at all. The Arminians you’re thinking of, though, are talking about prevenient grace being given at a much later time. I think they’re mixing up categories: the capability of free will to choose for good or evil, and the data for choosing good or evil (or maybe more specifically for loyalty to God or rebellion against God.)
People might not have accurate data, at this or that level of particularity, until long after God has given them the capability to use or abuse the data. That capability is the freedom of the will; the data is what the person is free to do with.
The capability and the data are both directly and by mediation only possible through God’s grace. That may be where the category error is happening: both are by God’s grace, so (wrongly) there is no distinction between capability and data.