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The hierarchical medical care structure is an efficient means of addressing some inadequate medical capabilities. Evaluating the several degrees of disease based on the physician’s diagnosis is a vital step in building a hierarchical healthcare treatment strategy. This study aims to offer different dynamic T-spherical fuzzy aggregation operators (AOs) for addressing multi-period decision-making (MPDM) situations in which decision-makers (DMs) have access to all information in the form of T-spherical fuzzy numbers (T-SFNs) spanning many time periods. AOs play a crucial role in decision-making, particularly when competing considerations are present. Developing suitable solutions for the aggregation process is a crucial challenge when dealing with unclear data. ”T-spherical fuzzy dynamic Einstein weighted averaging (T-SFDEWA) operator and the T-spherical fuzzy dynamic Einstein weighted geometric (T-SFDEWG) operator” are two innovative Einstein AOs. Several appealing properties of these AOs are addressed in depth. In addition, we present a strategy for addressing MPDM difficulties using optimum solutions. A numerical illustration of a hierarchical medical care system is provided to illustrate how the suggested method could be implemented. An authenticity assessment and comparative analysis is also provided to illustrate the effectiveness of the suggested method. In practice, the proposed AOs and decision-making technique are typically useful in multi-stage and dynamic decision analysis.