Maybe it’s just because I’m tired, but I can’t think of a way to pull this off natively within Airtable. Even using Zapier won’t get you very far. If I understand you correctly, what you’re essentially trying to do is turn event records in one table into checkbox fields in another table, with that second table being filled out by your staff via a form to indicate their availability for those events. Zapier (and Integromat) can do a lot of things, but I don’t think that creating fields is one of them. I haven’t tried using the Airtable API yet, but I’m not even sure it can be done at that level.
In lieu of creating fields on the fly, you could set something up where the form has checkboxes for events, but those checkbox states end up converting into record links in Airtable between the event records and the staff. I’ve got a very very very rough idea of how you might be able to use a combination of Jotform and Zapier to pull this off, though it’s definitely gonna take a while to set up, and it might require On2Air: Forms (a product by @openside) to make it all work.