I believe there should be some kind of logician, mathematician, philosopher, or any ancient thinker around the time of moses, jesus, or muhammad.
I have been trying to find any record that shows the presence of them and their contributions/influence towards the creation of fundamental parts of those religions. Sadly, because most of the starting points of those religions were heavily revolving around liberation and salvation of lower classes and poor people, many of important characters that I found are traders, rebelling nobles, and non-scholar characters.
This is my opinion but I think the presence/nonexistence of this record can provide a supporting fact towards the argument of whether there is a bridge between religion and science or not.
I think you have some fundamental conceptual problems with the kind of questions you are asking.
Firstly, I will confine myself to Christianity, as that is my speciality. One of the main figures in earliest Christianity would be Paul. Paul demonstrates a considerable depth of learning in the judaism of his time, as well as familiarity and engagement with Hellenistic learning of the period. His work is not intellectually light-weight by the standards of his time by any means.
Secondly, it is a misconception that earliest Christianity only penetrated the lower classes. For example, E.A. Judge finds that of 91 named individuals in the NT connected with Paul, 1/3 have names that likely indicate Roman citizenship, which, based on comparative data, is statistically quite high. For the context, this is generally an indicator of high status. Similarly, he identifies 40 persons who supported or sponsored Paul, all likely persons of social status and wealth.
Thirdly, the application of this to the "religion/science" divide is deeply suspect. The notion of "science" and "scientific method" current today is a philosophical development that would be anachronistic to project back to the 1st century. It is, in Western history, a consequence of theological and philosophical ideas. The idea of irresolvable conflict between "religion" and "science" is arguably a 20th century construct. I doubt whether simply locating a scholarly or learned person close to the source of a religious innovator contributes much to discussions of religion and science.