Put Trafficking Victims First Act of 2022 This bill sets forth provisions intended to help assess the prevalence of human trafficking in the United States and improve support for victims of trafficking and service providers. The Department of Justice (DOJ) must work with federal entities and other stakeholders to do the following: establish a working group to improve the collection and analysis of data on the incidence of trafficking, report on efforts to develop methodologies to determine the prevalence of human trafficking, and survey survivors to estimate the prevalence of human trafficking and improve services for victims. DOJ must also report on efforts to increase restitution to victims of trafficking.