Have you ever been reached by a customer whose profile you weren't expecting?

When I started working on my product, I was quick to determine my ICP: medium to large, digitally-heavy companies that struggle with hiring skills (my product is a skill management system and I figured these companies lacked the ability to nurture skills internally). However, as I interviewed users, I quickly found myself in a catch-22 situation: my most likely customers' requirements (SSO, white label, soc2, and pentest certifications, etc) would likely bankrupt me before I could have any deal closed. Lately, however, I've been approached by companies that didn't fit my ICP at all: universities and consulting firms. The former would like to use the tool to map the expertise of its staff, while the latter wants to use it to solve allocation issues I wasn't even aware of! While I don't feel my product is the right one for universities, the idea of pivoting the tool to attract consulting firms appeals to me. The problem they face seems more recurring and many don't have all the requirements an Enterprise would have. Customer profiles are important, but they are not as important as getting live. Do you have any stories of a customer coming from an unlikely place? What did you do?