The e-commerce industry has experienced significant growth in the past decade, particularly post-COVID. To accommodate such growth, the parcel delivery sector has also grown rapidly. However, there is a lack of study that properly evaluates its social and environmental impacts at a large scale. A model is proposed to analyze such impacts. A parcel generation process is presented to convert public data into parcel volumes and stops. A continuous approximation model is fitted to estimate the length of parcel service tours. A case study is conducted using New York City (NYC) data. The parcel generation is shown to be a valid fit. The continuous approximation model parameters have R2 values of 98% or higher. The model output is validated against UPS truck trips. Application of the model to 2021 suggests residential parcel deliveries contributed to 0.05% of total daily vehicle-kilometer-traveled (VKT) in NYC corresponding to 14.4 metric tons of carbon equivalent (MTCE) emissions per day. COVID-19 contributed to an increase in parcel deliveries that led to up to 1 064.3 MTCE of annual greenhouse gas (GHG) emissions in NYC (which could power 532 standard US households for a year). The existing bike lane infrastructure can support the substitution of 17% of parcel deliveries by cargo bikes, which would reduce VKT by 11%. Adding 3 km of bike lanes to connect Amazon facilities can expand their cargo bike substitution benefit from a VKT reduction of 5% up to 30%. If 28 km of additional bike lanes are made, parcel delivery substitution citywide could increase from 17% to 34% via cargo bike and save an additional 2.3 MTCE per day. Cargo bike priorities can be set to reduce GHG emissions for lower-income neighborhoods including Harlem, Sunset Park, and Bushwick.