Using The Burn Test to Identify Plastic Materials is one way. From the link:
To initially determine whether a material is thermoplastic (meltable)
or thermoset (non-meltable) type, heat a metal or glass stirring rod
until it glows red or orange (to about 500°F / 260°C) and press it
against the sample. If the sample softens, the material is a
thermoplastic; if it does not, it's probably a thermoset.
Next, hold the sample to the edge of a flame until it ignites. If no
flame is produced quickly, hold the sample in the flame for about 10
seconds. If the material burns, note the color of the flame, the
nature of the smoke, the presence of soot in the air and whether,
while burning, the sample drips.
Next, extinguish the flame and cautiously smell the fumes. To identify
the odor, samples of known plastic samples for comparison can be most
helpful. Finally, check your observations against the known
characteristics of each plastic as shown in the table below. Once you
have made a tentative identification, it is usually desirable to
repeat the flame test once or twice to confirm the results of the
original identification. Remember that additives may affect results.
For example: flame retardants can mask the polymer material's normal
flame & smoke burning characteristics.
However, remember ABS and PLA aren't the only types of filament.
ABS and PLA have different melting points and smell different when melting. Maybe try melting little bits on a soldering iron or stove top. The smell could give it away. Just don't breathe in the fumes, it can be toxic, also molten plastic particles in lungs aren't great either. I'd recommend contacting the supplier.
No markings complicates matters. Not very professional of the supplier. Smelling without breathing in fumes, just don't put your face directly over the fumes, just hold it away from your face and sniff sniff the air. if the smoke curls are going into your nose you are doing it wrong.