Is there a way to measure the attic square footage without having access to the actual attic?

There are two other methods to measure an attic's square footage but they are less accurate than going into the attic.

Building Code defines the attic as length x width, floor of the attic. That produces a "square footage" number. That's also how ventilation manufacturers generally define the size of an attic.  It's the most accurate measurement of the space we are trying to vent. Another measurement method that could work is viewing the footprint of the house looking at the house from the sky. It is less accurate but it does provide at least a measurement to work with. Another method to measure the attic without going into the attic is counting the number of "squares" of shingles to be installed on the roof. A "square" of shingles covers 100 square feet. This method, however, is once again less accurate then actually measuring the floor of the attic itself.  Air Vent would not recommend that an attic inspection be skipped by the roofing contractor just because a sky view of the roof or the number of "squares" of shingles to be installed are being used as the measurement tool for attic size.(and, thus, attic access is not needed by the roofing contractor).