The novel coronavirus SARS-CoV-2 emerged in China in December 2019 and has rapidly spread around the globe. The World Health Organization declared COVID-19 a pandemic in March 2020 just three months after the introduction of the virus. Individual nations have implemented and enforced with varying degrees of success a variety of social distancing interventions to slow the virus spread. Investigating the role of non-pharmaceutical interventions on COVID-19 transmission in different settings is an important research. While most transmission modeling studies have focused on the dynamics in China, neighboring Asian counties, Western Europe, and North America, there is a scarcity of studies for Eastern Europe. This study starts to fill this gap by analyzing the characteristics of the first epidemic wave in Ukraine using mathematical and statistical models together with epidemiological and genomic sequencing data. Using an agent-based model, the trajectory of the first wave in terms of cases and deaths and explore the impact of quarantine strategies via simulation studies have been characterized. The implemented stochastic model for epidemic counts suggests, that even a small delay of weeks could have increased the number of cases by up to 50\%, with the potential to overwhelm hospital systems. The genomic data analysis suggests that there have been multiple introductions of SARS-CoV-2 into Ukraine during the early stages of the epidemic with eight distinct transmission clusters identified. The basic reproduction number for the epidemic has been estimated independently both from case counts data and from genomic data. The findings support the hypothesis that, the public health measures did not have a decreasing effect on the existing viral population number at the time of implementation, since strains were detected after the quarantine date. However, the public health measures did help to prevent the appearance of new (and potentially more virulent) SARS-CoV-2 variants in Ukraine.