Warm intro or nothing — cold-emailing a family office is the fastest way to get filtered out permanently. They invest in people they (or someone they trust) already know.
So do the unglamorous work: publish your thinking consistently, show up where they gather, and get one trusted mutual connection to vouch. And know which type you're approaching — an operator-turned-allocator wants to re-underwrite your deal personally; a professionalized office wants an IC memo. Same money, completely different approach.