Asking someone for an informational interview is an opportunity to build a reciprocal relationship with that person. It’s a chance for someone to get to know you and for you to learn more about them. What you did was not to ask for an informational interview; instead, you
essentially asked for a job lead. If the person to whom you sent the inquiry didn’t know of any appropriate available positions, there was no reason (from their perspective and based on your ask) to continue the conversation.
What could work better? First, a more nuanced approach will take you further. People are savvy enough to understand that part of the reason you are reaching out is likely because you are considering a career move, but the focus should be on relationship-building and information-sharing in both directions, not on landing a job. Letting someone know that you would love to speak with them briefly because you find their work meaningful and their career path interesting will help you develop a sustainable relationship rather than a transactional one.
Second, while a short paragraph sharing a bit about your professional background will provide context to the person with whom you hope to meet, it is always best to wait to send your resume to someone until that person asks for it. Sending your resume from the get-go reinforces the idea that you simply want that person to find you a job rather than truly wanting to develop a professional relationship.
Third, have lots of questions ready to go. Doing research about the person, their professional background, and the organization with which they work will help you to prepare questions that will allow the conversation to flow while also showing that you’ve prepared well. For example, you might ask how someone made a particular transition from one position to another, or you might ask what they love most or find most challenging about their work. Perhaps they could share information about where they foresee opportunities for growth in their field or what they wish someone had shared with them when they were considering their current position.
Fourth, be ready to answer a version of “Tell me about yourself.” This seems so easy, but it trips up so many people and prevents them from starting a conversation with confidence. Being able to share where you’re coming from, where you are now, and where you hope to go next—and doing so in an engaging, concise way—will ensure that you start your discussion off on the right foot and with direction.
Finally, and in the spirt of reciprocity, it is always best to ask someone if they have other people they would recommend you meet—and for you to offer to do the same for them. The opportunity to broaden your network and also to make connections for others will not only support your job search, it will strengthen your professional community for years to come.