Premise 1 Every human choice or action is driven by past events.
Premise 2 We do not control past events.
Conclusion 1 Human free will does not exist.
From my perspective, the syllogism seems simple to the point where it is irrefutable. What do we think?
There are some issues with how you drew the conclusion as well as semantics of the word 'we'.
So, premise 1, even if proven to be true, doesn't exclude other factors in the choice-making process. It states that past events are part of it.
Premise 2 doesn't make clear who 'we' are because if one individual was or wasn't in control of certain past events it doesn't necessariy equate to 'we' being or not being in control as a whole group. Equally, even if 'we' the collective were in control in a hive-mind type thing, free will for the individual surely would be significantly limited.
The conclusion implies you had a premise specifying that free will is or isn't contingent on something (such as control of past events, which is probably what was implied) however the direct way you linked premise 1 and premise 2 to the conclusion isn't irrefutable at all, it's inconherent based on written words in your syllogism. You maybe needed a first conclusion to that syllogism to use as a premise in a future one, then you may evolve it to draw the conclusion you had there (with another premise on the new one).