What ways are there to disrupt spellcasting in 5e?

[ProsecutorGodot]

Because you (the PC) doesn't want to be the first to act in a hostile manner but won initiative? And to me that sounds more like the DM screwing with you really. I would literally be like 'dude, is he casting a spell or not?'

And I would ask you to make a check to see if you can recognize a spell or not, your PC doesn't have the knowledge of you as a player, he sees a robed man waving his hands around and practically screaming out unintelligible words. You would be told either "you've spent enough time with party wizard (or are party wizard) to recognize that these sounds and motions are completely unconventional for typical magic casting, you are confident that he's not actually casting a spell" on a success or "With as hectic as this fight has been, and the fact that you have seen him casting magic before, you can't be sure if this is a spell you haven't seen before or a bluff." on a failure.

If your trigger is trying to pre-empt the result of those actions, you don't get to know the result before you react.

Which is why I'm against the idea that you could set this type trigger in most cases*, it's metagamey and relies far too much on the structure of the game rules to define your in world actions and not enough on the potential realism of the scenario you're in.
*except in the cases where your readied action would reasonably be able to pre-empt the expected trigger without breaking the established chain of events, such as casting Silence instead of shooting an arrow.