The permissibility of investing in a company, whether a private or a public company, depends on factors not raised in your question, such as the nature of the company’s operations. I would therefore assume that those requirements have already been covered.
An IPO is understood as the process whereby a private company becomes a public company. I would therefore understand the purchase of IPO stocks in a company prior to debut to be a case of purchasing stock in what remains up to that moment, for all intents and purposes, a private company. In principle I cannot see anything objectionable in that.
Having said that, I must add that as long as the pre-debut purchase of shares does not violate any applicable laws, and does not in any manner involve dishonesty and misrepresentation, it will be permissible.
As for options, of both the call and put varieties, they are not permissible.