No. The "next block" is not very meaningful in Simulink: everything logically happens at the same time for continuous systems (except as modified by memory blocks or delay blocks or rate transition.)
Simulink groups blocks together in order to calculate algebraic equations that need to be satisfied to make the blocks work together. The blocks are not done individually: they are done as a group.
There is an ordering in Simulink, but not one that you have likely ever paid attention to; it has to do with ordering blocks so that datatypes can be made consistent.
Simulink has a debugging mode; perhaps you want to use that.
Perhaps what you need for your purpose is to use a MATLAB function that calls sim() for the model, specifying a StartTime and StopTime, and setting model parameters; when sim() returns you could use the normal graphic facilities to get user input about what they might want to change. You can then set model parameters using set_param(), and then sim() another time slice.