Many articles has been wrote abouy this topic, but the question is really necessary to accurately know the εr of the laminate?
A big accuracy is needed only if you design High Q, sharp, narrowband circuits; but in this case is also important to know how the εr change vs. temperature, vs. R.H.% etc.
Only a moderate accuracy is required for microstrip and stripline design. So the info ( the answer) can be found on the documentation rather than into the measurement.
You may do a rough estimation just looking the laminate.
Does the dielectric look like PTFE? (if yes probably εr is around 2.2...2.6)
Does the dielectric weight more than Rogers 5880 or similar (more weight means higher εr)
Does cutting the material destroy the cutter blade? if yes the laminate contains ceramics, εr>6 , probably 10.
Be confident that exist few class of εr : the 2.2...2.6, the 4.5 (G10, FR4), the 6 and the 10 (Alumina compatible).
It's rare the case that your laminate is outside the 4 classes.