Compare concentrations using LC/MS
You can indeed find the conversion (not the absolute concentrations), even without calibrating the system.

At time t = 0, take an exactly measured volume of reaction mixture (e.g. 1 mL) and dilute it in a volumetric flask with water and/or acetonitrile to an exact volume (e.g. 100 mL).

Inject an exact volume (e.g. 50 uL) of the diluted solution in the LCMS and note down the (UV-based) peak area of the limiting reagent. This is your ${A_0 = \epsilon \cdot C_0 \cdot k}$, where ${C_0}$ is the concentration of your limiting reagent at this time, and ${k}$ is a constant related to the sample size and dilutions.

At any time t, do exactly the same as above, and you get an area ${A_t = \epsilon \cdot C_t \cdot k}$. Under these conditions, ${k}$ is the same, and of course so is ${\epsilon}$.

As you know, the conversion is ${y = 1 - \frac {C_t}{C_0}  = 1 - \frac {A_t}{A_0} }$.