The section for buying gear only calls for an availability test when buying off the books (Pg. 418 "To purchase an item off the books, make an Availability Test").
That implies that buying something on the books like a normal person (as opposed to a SINless violent criminal) would not require an availability test. My guess for that process? Just matrix search for at most a few hours, automatically find what you want, decide to buy it, have your SIN checked by a R1-R3 scanner, have your applicable license checked (if it's Restricted), the system ties the purchase to your SIN/License, ownership of the item is transferred to your persona, and the item is delivered to you as per the delivery time table.
In game-terms, I think that the combination of risking your fake SIN and licenses getting burned, along with possibly losing all money on credit accounts associated with that SIN, along with tying the item to the SIN (possibly your real one if you're a SINner), is an appropriate trade-off for skipping an availability test.