During acute infection with hepatits B the B antigen is the first to rise (obviously as it is the infectious particle), and then the earliest antibody to form is the acute phase hepatitis B core antibody. This occurs at approximately 4-6 weeks and remains elevated indefinitely.
Next is the acute phase antibody (Ig-M) HBs-aby which rises then begins to drop in phase with the surface antigen.
There exists a window between 20-24 weeks post infection where screening tests will detect core antibody only as the surface antibdy (Ig-M) and surface antigen are declining and the chronic (Ig-G) antibody to the surface particle is not yet at detectable levels. Hence, HBs-ag and HBs-aby negative and HBc-aby positive.
If you request the acute and chronic phase antibodies to the surface particle it will likely be detected, but a simple screening test may miss it.
I hope this is helpful.