In logical progression, what things does a person need to know to design a robust opamp from BJTs
Questions like this can be difficult to answer because a lot of design is understanding why not to do it "the other way".  You can't see this by looking at the 741 circuit because these other topologies simply aren't there.

But a reasonable answer would be to look at how textbooks approach this.  Clearly writers of these books have to determine at least some base level of knowledge that must be taught before they can approach the 741 in detail.

Look at the fairly standard Microelectronic Circuits textbook by Sedra/Smith.  Section 12.3 is "The 741 Op-Amp Circuit".  So presumably, you would have to know at most everything up to this point in the book from the time they describe the BJT.  This should provide an upper limit for understanding the 741.

But I would like to remark that it is a long road from understanding how a circuit works to understanding why it was designed that way then further to being able to design it yourself.  It is a worthy trip to make, just not a short one.