Step 1: Recall the primary immune response.
During the first exposure to an antigen, naïve B lymphocytes are activated and initially produce
\[
\boxed{\mathrm{IgM}.}
\]
Step 2: Identify the correct immunoglobulin.
After class switching, antibodies such as IgG, IgA or IgE may be produced depending on the immune response.
Therefore, the first antibody produced during a primary immune response is
\[
\boxed{\mathrm{IgM}.}
\]
Hence,
\[
\boxed{(C)}
\]
is the correct answer.