To determine the quantitative relationship of charge, you need to be able to measure charge. But at the beginning there is no absolute scale of measurement. There is no “Colomb”. You must make measurements compared to a reference of unknown, but consistent value.
For example, charge an object and call the charge q0. Connect it to a spring or a pendulum or something with a known force. In this thought experiment, suppose we have a coil spring with a linear response. As you bring another charged object near q0, you can measure the attraction or the repulsion by the displacement of the spring.
The first task is to ensure that this is a consistent way to make measurements. Bring a charge q1 to q0. Note the distance between q0 and q1. Measure the displacement of the spring. Make a second measurement with charge q2. Make the first measurement again. Did it read the same as the first one? Wait for some time. Make the first and second measurements again. Did they read the same as the previous measurements? It’s imperative to make sure that your measurements are reliable even if they are crude. If one measurement influences the next, then maybe q0 is changed in the process. If the measurement changes in time, maybe charge decays.
With this apparatus, you can’t say that q1 is 1.2 Colombs. But you can say that for example, q2 displaces the spring by twice as much as q1. (That is, Δxq2 = 2Δxq1). You can also determine that when you combine two charges that independently behave like q1, they collectively behave like q2. (That is, Δxq2 = Δxq1 + q1.)
In symbols, Δxq1 + q1 = Δxq2 = 2Δxq1
It’s not hard to conceive of other measurements to show that the electrostatic force is a linear function with respect to charge. It also isn’t hard to conceive of measurements to show the inverse square relationship of distance and force. In the end, you only need a crude apparatus to discover $$F = k \frac{q_1 q_2}{r^2}.$$