Does software, and/or perhaps an actual device, exist that will give you the possible schematics of an analog circuit from measurements of the circuit?
If you start from a specifcation rather than a measurement, what you're describing is called circuit synthesis.
Synthesis is very common in digital design, where we usually work by making a description of the hardware behavior in a hardware description language and then using a synthesis tool to produce a digital logic circuit to implement that behavior.
In analog design, it's also possible to at least design subcircuits or circuit blocks using synthesis.
For example, Genesys is a software package from Keysight that can synthesize filters for RF frequencies.
For lower frequencies, some chip vendors provide web tools to generate circuits using their chips to provide certain functions. TI's WeBench is probably the most prominent of these, used to produce switching power supply designs or op-amp active filters.