Partially yes, though doing it today would probably be hard.
The problems here are threefold:
No male gamete donors
This may not be a problem. Viable bi-maternal embryos have been created in a variety of species at this point. The fact that both the gametes would be coming from the same parent is another problem, namely...
Parthenogenesis doesn't tend to work for sexed creatures, even when artificially induced, because of imprinting locations in our genetic sequences. We're big into recombination, because it gives us additional avenues for beneficial mutation and recombination, without reinforcing negative traits.
Potentially, you could use CRISPR to modify the genes in one of the manipulated gametes or eggs to increase heterozygosity. This is strictly experimental right now, though, and would be unlikely to produce viable offspring in this "one chance or you'll miss it" preservation of the species unless a desperate effort were made. Cloning potentially buys you some time here.
This is probably wholly unnecessary. While a Thylacine is part of a largely-extinct family, as long as its reproductive characteristics are sufficiently close to an extant mammal, a surrogacy could probably be maintained.
So, if this were to happen today, the species would probably be done for, though genetic samples could be preserved for cloning/recombination at a later date. We're very close, however, technologically, to being able to recover the species from a single specimen.
The one caveat - no male specimens, until and unless we figure out how to manufacture a Y-chromosome from whole cloth. We could potentially find a close relative and do some substantial genetic engineering on its gametes, but that is not something we're close to being able to do right now.