Is it appropriate to apply for assistant professor positions a few months before obtaining my PhD? I am finishing my PhD at a famous research institution located in Europe. I am quite delayed due to COVID-related disruptions, which forced us to devote most lab equipment to vaccine development and trial assessment instead of doing some experiments I needed to validate my hypotheses.
Nonetheless, I will obtain my degree within the next few months. My thesis has already gone through a mandatory internal assessment process, which is similar to peer review. And my advisor has already appointed examiners.
I have some interesting publications in good journals (Nature Comms and equivalent ones), but a big part of my thesis is only published as a preprint in medRxiv. My findings are very novel and, in the words of my supervisor (who is a big name in the field), it's a major breakthrough. We've contacted other big names in the field, who are also really interested in this new approach, and they are helping to validate things. We already have enough for submitting to a top journal, which is good.
My advisor and his peers are writing grant applications and preparing clinical trials based on my findings. I am interested in continuing with this line of research, but I will need to find a different host institution once I graduate. I would like to continue as soon as possible in order not to loose a head start on my own ideas.
I am a bit confused with research-oriented Assistant Professor openings. Is it appropriate to apply at this stage? I have contacted one US professor behind an open position, and he encouraged me to apply. However, is this the norm for most American and European positions?
In most biology/biological sciences departments in the US and Canada it would be unusual for someone to be hired into a tenure-track assistant professorship immediately following their PhD; most candidates would have at least a year or two of postdoctoral experience. (This may be different in biomedical and/or clinically oriented programs). If you have a spectacular research record that could make you an exception.
Postdoctoral experience is less expected in math (although 1-2 years is probably still the median), and even less in statistics; this is probably also the case in other fields such as engineering where people with a fresh PhD can get well-paying jobs in industry.
It doesn't hurt to apply for such positions, but I would say if would be safer to at least consider a few post-doctoral positions as a backup plan.
Finally, as with most questions like this, you will get the most relevant advice from your supervisor and colleagues in your lab/program; they know the most about the norms of your particular sub-field and geographic region. Unless you have some particular reason not to, you should probably ask them.

Here is some data from a reasonably recent survey of (mostly North American) ecologists (note, this paper was contentious because of the way it handled gender and informed consent of respondents):

Recently hired TT assistant professors of ecology typically were about 4 years post-Ph.D. at the time of hiring (mean 4.2 years, median 4). 69% had anywhere from 2 to 6 years of post-Ph.D. experience, with a range from 0 to 11 years of post-Ph.D. experience. The majority of ecology faculty job seekers also are 2–6 years post-Ph.D.


These data are consistent with a job market in which most hiring institutions prefer applicants with at least a year or two of post-Ph.D. experience. But once you have a few years of post-Ph.D. experience, the marginal value of additional post-Ph.D. experience appears to be low at best, though it's hard to say precisely based on the available data.

Fox, Jeremy. “A Data-Based Guide to the North American Ecology Faculty Job Market.” The Bulletin of the Ecological Society of America 101, no. 2 (2020): e01624. https://doi.org/10.1002/bes2.1624.