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How to find out the purpose of play of a con game?

In a con game, or other one-shot with strangers, I often meet the problem that I don't really know how the game master and the other players are going to approach the game, or would like me to do the same. An archetypal example is Call of Cthulhu. Are we there to...
* try to, as players, solve the mystery and stop the evil, with success and failure as real possibilities, and our skills and luck as the deciding factor?
* create and appreciate a story like those by Lovecraft (maybe aside from the blatant racism etc.), trying to stick to the genre conventions and play so as to eventually reveal the horrific?
* try to get into the headspace of the player characters, immersing ourselves into the roles of more-or-less normal people facing the supernatural and unexplainable?

All of these are possible games and can be interesting, but I do want to know which one I am playing. In my experience, asking directly does not produce results: "do whatever" or "everything at once" are typical answers, but the behaviours of the game master and maybe other people during the game often reveal something else. Call of Cthulhu is just an example here. The same problem applies to D&D and many other games, usually with slightly different alternatives as to what the creative agenda might be.

I suspect the reason is that the game master in question might only know one creative goal and might thus see roleplaying as a singular activity with a fixed goal, rather than seeing the multitudes of creative possibilities the hobby has. Or maybe they just lack the vocabulary to express such issues.

How can I, as a player, effectively find out the creatives goals of a particular con game or similar one-shot?