Considering that the target is a quite large binary, are there some efficient ways to trace functions that get an input from the outside (command line, network, files etc.) in a dynamic approach? Consider that the target binary runs on Linux.

I'll give a small artificial example: there is a closed-source web browser and I want to find a function address in which the HTTP requests are processed. Is static RE is the only viable option to spot this function out of thousands of other functions?

Besides, I've tried to use ltrace and strace, but these utilities don't give an ability to spot the specific function address, it just prints out the lib/system calls.