What is a more professional term for the phrase 'back-of-the-envelope' calculation, used by scientists and such as a word for a very basic, general first calculation?
[Making a] Zeroth-order approximation [Wikipedia].
In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth.
This not only has the advantage of sounding more formal, it implies a pathway toward more formal approximations.
In some cases estimate fits. I prefer rough estimate to reinforce the notion of arbitrary assumptions. With respect to your comment, initial estimate has a nice ring to it, and easily leads to ... based on which is often appropriate.
Back-of-the-envelope calculation is more generally accepted than the (presumably only British) synonym fag-packet calculation (or -- sketch etc.) Another useful but fairly informal word is guesstimate, which you'll find in plenty of dictionaries.