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Unfortunately this is not the case: https://www.nature.com/articles/s41598-020-63707-z
"Measles virus evolved from the then-widespread rinderpest virus most probably between the 11th and 12th centuries."
https://journals.plos.org/plosone/article?id=10.1371/journal...
In theory, it's very much doable. We brought back an extinct cowpox virus a while ago using mail-order DNA. Did you know that Smallpox's nucleotide sequence is freely available online?
There's a gulf between assembling a vaccine - which is a commonplace technology, and assembling a viable infectious viral particle.
Being able to order all the oligos of a viral sequence isn't even step 1.
https://www.ncbi.nlm.nih.gov/nuccore/NC_001611.1
As for getting the nucleotides themselves, there are numerous services for ordering oligonucleotides which you can "stitch together." I think this used to be done with phosphoramidite synthesis, but the article I linked says they used plasmid synthesis, and ordered from ThermoFisher.
https://www.thermofisher.com/us/en/home/life-science/cloning...
I'm not sure what the price would be on this (I would imagine very high?), but it has to be cheaper than phosphoramidite chemistry. Nevertheless, the price of doing this sort of things w/ plasmids is plummeting.