TOA distance resolution
There's no such thing as a free lunch. So no, you can't have higher resolution than what you've been given. However, there are a few points to ponder:


Practically speaking you can upsample the capture and thus gain resolution, because any system has a little jitter and/or is asynchronous, and we'll assume you took multiple measurements. So you've effectively added more samples at different timing positions.
If the TOAs are "absolute" (that is, you know the transmit time), then the probability distribution for one TOA is a hollow sphere around the receiver with a diameter of the distance calculated. The intersection of multiple spheres from multiple receivers is used to resolve the transmitter's position, and you gain resolution according to how many spheres there are, because you are effectively adding more samples.
If the transmit time is not known, then pairs of TOAs to multiple receivers can be used to generate TDOAs (time difference of arrival). A TDOA produces a hyperboloid sheet of probability distribution between the receivers. The intersection of multiple sheets is used to resolve the transmitter's position, and you gain resolution according to how many sheets there are, because you are effectively adding more samples.