USB female type A that "floats" on a PCB
What you are looking for is called a "mid mount" connector. They exist in the type A receptacle but will most likely be the USB 3.0 type instead of the 4-pin USB 2.0 type that you are probably thinking about. I used a search phrase of "mid mount USB Type A connector" and found several suitable styles.

Any mid mount connector that you choose to use should have metal shell fingers that sit on pads on the surface of the circuit board that get soldered to secure the connector. Something just mounted by four leads as you made in your picture will not standup to use of the large Type A plug that would mate with it.