Are there any necessary or sufficient conditions for getting a faculty position?
Previously, I suggested that a key element is actually dumb luck: being in the right place at the right time. But that is not my focus here.
Twenty years ago when I was struggling to find a faculty job the mythology was that you had to have at least two PRLs and get an invited talk at an APS March Meeting. And doing a postdoc at certain places (e.g. ITP Santa Barbara) would help...
Now the mythology seems to be that you need to have Nature and Science papers....
But, this in actually not the case.
This is not a sufficient condition.
Search committees want to hire someone who can lead an independent research program and can move into new areas.
Several department chairs have said things to me along the lines of "It is amazing how we interview some candidates who have impressive publication lists involving papers in luxury journals but when we actually talk to them we quickly lose interest. We find they lack any sort of big picture. Some cannot even articulate why their own papers are scientifically important, let alone future directions. It seems they have been a student or postdoc in some big group and they have developed some narrow (but important) technical expertise (e.g. device fabrication, running computational chemistry codes, using an STM, ...) that is indispensable to the group."
I find this quite sad. It is sad for the individuals. All the hard work in the hope of getting a faculty position will have gone to waste. I also find it sad when faculty don't prioritise training group members.
How can you stop this being you?
Read papers, including outside your actual research project.
Talk to people in different research groups about what they and you are doing.
Go to seminars, even when you are busy.
But, particularly write papers yourself.
If you are the first author you really should write the first draft, including the introduction yourself. Don't let your boss (or someone more experienced) do it or expect them to.
Your draft may be poor and get heavily edited or even discarded completely. But you will learn from the process and with time confidence and competence will follow.