Urban Progress Act of 2018 This bill amends various provisions of law and sets forth new provisions to promote economic development, expand employment opportunities, reduce gun violence, and limit the impact of poverty. Among other things, it: makes permanent the work opportunity tax credit and increases it for employers who hire ex-felons; establishes grants to promote commercial development in underserved communities, to provide career training programs, and to support summer employment opportunities for youth; increases tax deductions for business start-up expenditures and for corporations' organizational expenditures; establishes a working group to develop a national plan to reduce child poverty; increases Supplemental Nutrition Assistance Program benefits, when school is not in session, for households with minor children; increases the child tax credit for low-income taxpayers; creates a process to expunge and seal certain youth criminal records; authorizes grants to prevent juvenile delinquency and criminal street gang activity; makes trafficking in firearms a stand-alone criminal offense; requires annual reports on the public health effects of gun violence; broadens the categories of prohibited persons who are barred from receiving or possessing firearms; requires states to submit mental health and criminal history records to the National Instant Criminal Background Check System; requires federal agencies and departments, including courts, to certify whether they provided disqualifying records of prohibited persons; prohibits firearm transfers between private parties unless a licensed dealer first conducts a background check; requires gun owners to report lost or stolen firearms; and prohibits licensed gun dealers from transferring firearms to unlicensed persons prior to background check completion.