Forecasting multivariate time series data, which involves predicting future values of variables over time using historical data, has significant practical applications. Although deep learning-based models have shown promise in this field, they often fail to capture the causal relationship between dependent variables, leading to less accurate forecasts. Additionally, these models cannot handle the cold-start problem in time series data, where certain variables lack historical data, posing challenges in identifying dependencies among variables. To address these limitations, we introduce the Cold Causal Demand Forecasting (CDF-cold) framework that integrates causal inference with deep learning-based models to enhance the forecasting accuracy of multivariate time series data affected by the cold-start problem.To validate the effectiveness of the proposed approach, we collect 15 multivariate time-series datasets containing the network traffic of different Google data centers. Our experiments demonstrate that the CDF-cold framework outperforms state-of-the-art forecasting models in predicting future values of multivariate time series data suffering from cold-start problem.