For more than 50 years, Cuba has been one of the most important players in the field of international medical care in the Global South. Between 2013 and 2018, Cuba sent nearly 18,000 Cuban health professionals to Brazil within the framework of the More Doctors Program to assist during the Brazilian public health care system's state of emergency. This article focuses on local encounters and emergent socialities between Cuban physicians and Brazilian patients and medical staff. Their sensitive moments of interaction—with their embodied, emplaced, and political dimensions of past and present—hold the possibility of a fragile intersubjectivity that creates its own temporal and affective dynamics, undermining, for a moment, the prevalent care regimes.