Q. Should I be able to push up shingles on edge of new roof?
According to GAF Roofing manufacturer’s installation guide, the shingles should overhang the rake between 1/4” and 3/4”. 

Here’s their website that explains it better: https://www.gaf.com/en-us/document-library/documents/residentialroofing/shingles/glenwood/glenwood_shingles_application_instructions_english_spanish_french.pdf

Yes, you should be able to push the shingles up about 1”, but if they extend too far beyond the edge of the roof (especially in a high wind area like you live in) they’re more susceptible to blow off. 

Also critical is the correct number of nails per shingle. In high wind areas, 6 nails are required. 

GAF is a major Roofing manufacturer in the U.S., but I’d check with your shingle manufacturer’s instructions.