You ask an excellent question about the size of a single large cM match. I would always recommend that you consult the Shared cM Project to get a sense of the potential range for your match-size. It is at https://dnapainter.com/tools/sharedcmv4
Putting in 35cM to the "filter", it shows a 51% likelihood of between 4c1r to 8c or even further back. An 8c requires that you can both trace back to all your 10th generation ancestry, all lines. Highly unlikely that even one of you has such a complete tree. A 4c1r relationship is only slightly better; one of you needs to know all lines to the 7th generation and the other to the 6th.
My recommendation is to focus on doing the as much of the paper-trail to have at least all 8 g-gp's with surnames and better, all 16 gg-gp's. For the distant matches, you really need to get to at least gggg-gp's (all 64 of them), if you want to just use surname to identify a 5c match. Or, Once at all 16 gg-gp's, you can try to use shared-matches and triangulation in order to at least narrow down the part of your family pedigree the 35cM match relates to.
You might also review Dana Leed's "Leeds Method". See: https://www.danaleeds.com/can-the-leeds-method-help-me/
Good luck and stay safe,