The use of whole genome sequencing (WGS) to track the emergence of severe acute respiratory syndrome-related coronavirus 2 (SARS-CoV-2) variants across communities is increasingly prevalent. Given the varying levels of SARS-CoV-2 genomics capacity in public health laboratories worldwide, active participation in an external quality assessment (EQA) program is highly recommended. Here, we used the responses from the yearly SARS-CoV-2 WGS program (2021 to 2023), including both wet and dry-laboratory components, to evaluate the performance and the state of pathogen genomics readiness across Australia and New Zealand. We observe a significant increase in the capacity for SARS-CoV-2 genomic surveillance and capabilities based on the determined 'sequencing quality' criteria (genome coverage, pango lineage and F1 score). In particular, the fail rate assessed in the laboratories' performance in sequencing a negative SARS-CoV-2 EQA specimen dropped significantly over the years, suggesting successful intra-laboratory preventative measures in minimising cross-contamination at all sample processing and testing stages within their WGS workflow. In the three years of assessment, laboratories exhibited the lowest performance (fail rate of 50% for a SARS-CoV-2 positive specimen) in the first EQA offered in February 2021, and it improved in the following year. As more recent SARS-CoV-2 variants were included in the EQA specimen panel in 2023, we noticed a slight increase in the fail rate in the assessment for SARS-CoV-2 positive specimens, particularly for newer SARS-CoV-2 Omicron subvariant (XBB.3). This study finds that the WGS process is not the primary limiting factor in the genomics capacity among public health laboratories. Instead, it highlights that the bioinformatics analysis workflows following sequencing are the primary hurdles that must be addressed. Although the current WGS capabilities of public health laboratories seem to have progressed beyond their initial state during the early stage of the SARS-CoV-2 pandemic, the development of genomics capacity remains crucial in facilitating prompt and efficient responses to all emerging infectious diseases. Capacity-building activities such as an EQA, as described here, that aim at strengthening the pathogen genomics capabilities are valuable and should become a priority in guiding the full implementation of WGS in public health laboratories.