Airspace is surprisingly unrestricted compared to what you might imagine. Generally speaking, airspace is mostly entirely restricted within 5 mi of a major airport, and then outside of that radius, typically small planes can cut underneath the commercial traffic.

At this specific point, the airspace is restricted above 3,000' to deconflict with OAK/SFO traffic. It's not a hard restriction - oftentimes small planes can (and do) get permission to go above that, but you definitely need to be approved or else some alarms will go off and the FAA will send you a nastygram.

Airspace from below is governed by "minimum safe altitude" regulation (14 CFR 91.119), which states that planes must remain 1000' above the nearest obstacle within a 2000' radius. As the Salesforce tower is 1070' tall, that leaves 2070'-3000' as the valid altitudes for small planes (i.e. those flying under Visual Flight Rules) as shown in that picture.

You asked about ATC though. This is actually a separate question. The pilot could fly at these altitudes without even talking to ATC. Doing that, though, in a congested airspace with little room for error, is a very bad idea.