So the answer to my question is "No." You cannot prove Jesus is still alive via any empirical means.
For a basic primer on Paleontology, go here. We don't have faith that dinosaurs existed we have reasonable confidence due to the vast fossil record and other lines of data that clearly point to the same conclusion.
If you are going to make the claim that direct knowledge is a precursor to learning, you have brought most academic disciplines to a screeching halt. Forget history. Forget astronomy. Forget even a criminal justice system based on contemplation of evidence. If you really want to know if Jesus is alive do this while meditating talk to Him.
Finally, why do you believe something for which no empirical evidence? because I know what believing in Him has done for me, I was a lost soul without a purpose now I know that there is something better for me and I wouldnt trade Him in for nothing in this world. God bless