A priori estimation of sample size and subject accrual in multi‐site, time‐to‐event clinical trials is often challenging. Such trials are powered based on the number of events needed to detect a clinically significant difference. Sample size based on number of events relates to the expected duration of observation time for each subject. Temporal patterns in site initiation and subject enrollment ultimately affect when subjects can be accrued into the study. Lag times are common as the site start‐up process optimizes, resulting in delays that may curtail observational follow‐up and therefore undermine power. The proposed method introduces a Program Evaluation and Review Technique (PERT) model into the sample size estimation which accounts for the lag in site start‐up. Additionally, a PERT model is introduced into a Poisson‐Gamma subject accrual model to predict the quantity of study sites needed. The introduction of the PERT model provides greater flexibility in both a priori power assessment and planning the number of sites, as it specifically allows for the inclusion of anticipated delays in site start‐up time. This model results in minimal power loss even when PERT distribution inputs are misspecified compared to the traditional assumption of simultaneous start‐up for all sites. Together these updated formulations for sample size and subject accrual models offer an improved method for designing a multi‐site time‐to‐event clinical trial that accounts for a flexible site start‐up process.