Analysis of migration flows is crucial for understanding and forecasting social and economic trends. This paper presents an algorithm for obtaining migration estimates with minimal time delay (nowcasting) using Google Trends Index (GTI) search queries. The predictive power of the models is assessed across different periods, including one marked by the restrictions imposed due to the COVID-19 pandemic, which significantly impacted migration opportunities. The paper evaluates models for estimating migration from six different countries to Germany. The key findings are as follows: first, in periods free from external shocks, using a single search query such as «work in Germany» in the official language of the migration origin country, along with its 12-month lags in SARIMAX or distributed lag models, yields higher accuracy in migration estimates compared to SARIMA models. Second, during periods with external shocks, a multi-query distributed lag model, which incorporates additional search queries related to migration intentions, demonstrates superior predictive quality. Finally, the paper proposes an enhanced method for migration forecasting based on GTI data. It highlights the importance of using a distributed lag model, which includes multiple GTI time lags, rather than models with individual GTI lags. Models employing GTI with lags consistently show better predictive power than SARIMA models across all countries and time periods considered.