COVID-19 epidemic has been suppressed in Hungary due to timely non-pharmaceutical interventions, prompting a considerable reduction in the number of contacts and transmission of the virus. This strategy was effective in preventing epidemic growth and reducing the incidence of COVID-19 to low levels. In this report, we present the first epidemiological and statistical analysis of the early phase of the COVID-19 outbreak in Hungary. Then, we establish an age-structured compartmental model to explore alternative post-lockdown scenarios. We incorporate various factors, such as age-specific measures, seasonal effects, and spatial heterogeneity to project the possible peak size and disease burden of a COVID-19 epidemic wave after the current measures are relaxed.