Upsampling signal for cross correlation
A narrow-band filter may remove some of the bandwidth of the signal containing timing information of the signal's envelope modulation.  The narrower the filter, the more any tone burst will be smeared out in time.  Upsampling after the timing information is destroyed won't help much.  Using a wider bandwidth signal, channel, and filter, with perhaps a higher sampling rate to support that bandwidth, will help improve time estimation accuracy.

A chirp, or other large frequency modulation is one common method used to increase a signal's bandwidth to allow better timing estimation.

Also note that any real signal with a frequency near either DC or Fs/2 can face strong interference from it's negative frequency conjugate image in the frequency domain, as well as any of the images sidebands, which can also greatly distort the signal envelope and the envelopes timing information in the received sampled data.  A higher sampling rate can also help solve this problem for high frequency tones.  (And a longer sample window length for near DC signals.)