Highly transmissible SARS-CoV-2 variants have emerged throughout the COVID-19 pandemic, driving new waves of infections. Genomic surveillance data can provide insights into the virus\'s evolution and biology. However, delayed and limited regional data can introduce biases in epidemiological models, potentially obscuring transmission patterns. To address this issue, we used a novel, variant-specific back-projection model to estimate a distribution of likely infection times from sample collection times. We combined this approach with epidemiological modeling to estimate selection for increased transmission in a way that accounts for the uncertainty in infection times. Tests in simulations demonstrated that our method can make the inference of selection more reliable. We also applied our approach to SARS-CoV-2 data, where it excelled in smoothing and extending data from geographic regions or times with poor sampling. Overall, our method can aid in the reliable identification of mutations and variants with higher transmission rates.