People who use a phonograph regularly would be able to put the arm in the right place on most albums immediately -- by counting the shiny rings between tracks. At 33RPM (the 12" discs, 22 minutes per side) a 2 second gap is a complete shiny ring.

If your character has been drinking or is otherwise unsteady, it could take longer to find the gap accurately. Dropping the needle roughly is a good way to scratch the record. Want to add more misery? That scratch will be there permanently and audibly.