With the proliferation of time-series analysis in the healthcare sector, each new time series requires a new model to be fit and trained on those specific data. The vast majority of time-series forecasting approaches require a training dataset. There is very recent work on zero-shot forecasting---pretraining on one series and evaluating on another---yet its performance is inconsistent depending on the training dataset. In this work, we take a different approach and devise ForecastPFN, the first universal zero-shot model, pretrained purely on synthetic data. Drawing inspiration from TabPFN, a recent breakthrough in tabular data, ForecastPFN is the first forecasting model to approximate Bayesian inference. To accomplish this, we design a synthetic time-series distribution with local and global trends, and noise. Through experiments on multiple datasets, we show that ForecastPFN achieves competitive performance without ever seeing the training datasets, compared to popular methods that were fully trained on the training dataset.