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?