I see problems in several areas there.
As for material, NM is not OK outside.
590.4(A)(B) Feeders. Overcurrent protection shall be provided in accordance with 240.4, 240.5, 240.100, and 240.101. Feeders shall originate in an approved distribution center. Conductors shall be permitted within cable assemblies or within multiconductor cords or cables of a type identified in Table 400.4 for hard usage or extra-hard usage. For the purpose of this section, Type NM and Type NMC cables shall be permitted to be used in any dwelling, building, or structure without any height limitation or limitation by building construction type and without concealment within walls, floors, or ceilings.
This is not "in" a building.
You also need to adequately protect cords and cables from physical damage.
(H) Protection from Accidental Damage. Flexible cords and cables shall be protected from accidental damage.
Running unprotected across the parking lot ain't it.
What I have seen that works fairly well is to make a trough from 2x6s on each side of the cable and staked down to the asphalt with 1x3s every several feet to lock everything together and hold the cord in place.
I would also question the time constraints.
