What is the maximum age to get into academia, as a recent PhD / recent post-doc, in the US?
This is strictly speaking not an answer, since OP was asking about the US, but I felt sharing a European perspective may be of interest here as well. Flag if you feel I am straying off topic too much, and I will happily delete the answer.

ETH Zurich, presumably the premiere technical university in Europe (and one that often follows US procedure pretty closely), actually has an official policy on this.


  The academic age of assistant professors (e.g. without the time period of maternity leave, industry experience, military service, etc.) should be 35 years or under at the time of appointment.


Source

Note that they explicitly speak about "academic age", not biological age. Time spent as a postdoc counts against you, but time in industry or in maternity leave does not. Given that, there is (in theory) no biological limit to become assistant professsor if you have been doing "something else" before in your life, but I suspect in practice there is: at Swiss universities, there is mandatory retirement at age 65, and ETH presumably is not overly interested in investing into young professors that don't have too long until retirement anymore.

In Germany, a rule that I sometimes hear is that you need to become professor before the age of 40 or get out (where "professor" usually means W2 or W3 professor according to the German system). However, this is more of a guideline than a formal rule - I have certainly seen cases of people who got appointed with their first professorship after 40.